diff --git a/cypress/integration/deposit-admin.spec.js b/cypress/integration/deposit-admin.spec.js
--- a/cypress/integration/deposit-admin.spec.js
+++ b/cypress/integration/deposit-admin.spec.js
@@ -107,13 +107,13 @@
         cy.contains(deposit.status).should('be.visible');
         // those are hidden by default, so now visible
         if (deposit.status_detail !== null) {
-          cy.contains(deposit.status_detail).should('not.be.visible');
+          cy.contains(deposit.status_detail).should('not.exist');
         }
 
         // those are hidden by default
         if (deposit.swhid !== null) {
-          cy.contains(deposit.swhid).should('not.be.visible');
-          cy.contains(deposit.swhid_context).should('not.be.visible');
+          cy.contains(deposit.swhid).should('not.exist');
+          cy.contains(deposit.swhid_context).should('not.exist');
         }
       });
 
@@ -126,7 +126,7 @@
           let expectedOrigin = expectedOrigins[deposit.id];
 
           // ensure it's in the dom
-          cy.contains(deposit.id).should('not.be.visible');
+          cy.contains(deposit.id).should('not.exist');
           if (deposit.status !== 'rejected') {
             expect(row).to.not.contain(deposit.external_id);
             expect(row).to.contain(expectedOrigin);
diff --git a/cypress/integration/layout.spec.js b/cypress/integration/layout.spec.js
--- a/cypress/integration/layout.spec.js
+++ b/cypress/integration/layout.spec.js
@@ -183,7 +183,7 @@
     }).as('getSwhStatusData');
     cy.visit(url);
     cy.wait('@getSwhStatusData');
-    cy.get('.swh-current-status').should('not.be.visible');
+    cy.get('.swh-current-status').should('not.exist');
   });
 
 });
diff --git a/cypress/integration/origin-save.spec.js b/cypress/integration/origin-save.spec.js
--- a/cypress/integration/origin-save.spec.js
+++ b/cypress/integration/origin-save.spec.js
@@ -289,7 +289,7 @@
       .click();
 
     cy.get('.swh-save-request-info-popover')
-      .should('not.be.visible');
+      .should('not.exist');
   });
 
   it('should hide task info popover when clicking on the close button', function() {
@@ -308,7 +308,7 @@
       .click();
 
     cy.get('.swh-save-request-info-popover')
-      .should('not.be.visible');
+      .should('not.exist');
   });
 
   it('should fill save request form when clicking on "Save again" button', function() {
diff --git a/cypress/integration/origin-visits.spec.js b/cypress/integration/origin-visits.spec.js
--- a/cypress/integration/origin-visits.spec.js
+++ b/cypress/integration/origin-visits.spec.js
@@ -87,7 +87,7 @@
           .trigger('mouseout');
 
         cy.get('.popover')
-          .should('not.be.visible');
+          .should('not.exist');
       });
   });
 
diff --git a/package.json b/package.json
--- a/package.json
+++ b/package.json
@@ -55,7 +55,7 @@
     "@babel/plugin-syntax-dynamic-import": "^7.8.3",
     "@babel/plugin-transform-runtime": "^7.12.1",
     "@babel/preset-env": "^7.12.1",
-    "@cypress/code-coverage": "^3.8.3",
+    "@cypress/code-coverage": "^3.8.5",
     "autoprefixer": "^10.0.2",
     "axios": "^0.21.0",
     "babel-eslint": "^10.1.0",
@@ -66,7 +66,7 @@
     "clean-webpack-plugin": "^3.0.0",
     "copy-webpack-plugin": "^6.3.0",
     "css-loader": "^5.0.1",
-    "cypress": "^5.6.0",
+    "cypress": "^6.0.1",
     "cypress-multi-reporters": "^1.4.0",
     "ejs": "^3.1.5",
     "ejs-compiled-loader": "^3.0.0",
@@ -132,4 +132,4 @@
   "engines": {
     "node": ">=8.9.0"
   }
-}
\ No newline at end of file
+}
diff --git a/yarn.lock b/yarn.lock
--- a/yarn.lock
+++ b/yarn.lock
@@ -1486,13 +1486,13 @@
     through2 "^2.0.0"
     watchify "3.11.1"
 
-"@cypress/code-coverage@^3.8.3":
-  version "3.8.3"
-  resolved "https://registry.yarnpkg.com/@cypress/code-coverage/-/code-coverage-3.8.3.tgz#4bda76bbf07a01036ad58a60b6f9f86d6cb8c156"
-  integrity sha512-4R9bDS4CivckXaJudL5lKxXtB99LkO2RWE4a5M/P7VXGrXynQQDYbP07O9Jyjw/VjELWBV+xC3AOfYaU+wCHNQ==
+"@cypress/code-coverage@^3.8.5":
+  version "3.8.5"
+  resolved "https://registry.yarnpkg.com/@cypress/code-coverage/-/code-coverage-3.8.5.tgz#4071990abdeca780e30c9d15236aa28d00cbe610"
+  integrity sha512-JdMha0XttCmgzT+WegRhQITZpW9yfjwy6yEs1EU7qUws7v9kVPtP/9ZH+021f7kzyqbcPuVC0+pbfBxB5RlwmQ==
   dependencies:
     "@cypress/browserify-preprocessor" "3.0.1"
-    debug "4.2.0"
+    debug "4.3.1"
     execa "4.1.0"
     globby "11.0.1"
     istanbul-lib-coverage "3.0.0"
@@ -4304,10 +4304,10 @@
     debug "^4.1.1"
     lodash "^4.17.15"
 
-cypress@^5.6.0:
-  version "5.6.0"
-  resolved "https://registry.yarnpkg.com/cypress/-/cypress-5.6.0.tgz#6781755c3ddfd644ce3179fcd7389176c0c82280"
-  integrity sha512-cs5vG3E2JLldAc16+5yQxaVRLLqMVya5RlrfPWkC72S5xrlHFdw7ovxPb61s4wYweROKTyH01WQc2PFzwwVvyQ==
+cypress@^6.0.1:
+  version "6.0.1"
+  resolved "https://registry.yarnpkg.com/cypress/-/cypress-6.0.1.tgz#86857ca2f527c3723575737deab42fd8f2a209df"
+  integrity sha512-3xtQZ0YM65soLgKQUgn2wg2IbWsM6A2yBg6L4RF31mZHr5LNKdO2/9sgiwxEVMKu2C2m6+IQ75zHP41kZP5rPg==
   dependencies:
     "@cypress/listr-verbose-renderer" "^0.4.1"
     "@cypress/request" "^2.88.5"
@@ -4875,6 +4875,13 @@
   dependencies:
     ms "2.1.2"
 
+debug@4.3.1:
+  version "4.3.1"
+  resolved "https://registry.yarnpkg.com/debug/-/debug-4.3.1.tgz#f0d229c505e0c6d8c49ac553d1b13dc183f6b2ee"
+  integrity sha512-doEwdvm4PCeK4K3RQN2ZC2BYUBaxwLARCqZmMjtF8a51J2Rb0xpVloFRnCODwqjpwnAoao4pelN8l3RJdv3gRQ==
+  dependencies:
+    ms "2.1.2"
+
 debug@^3.1.0, debug@^3.1.1, debug@^3.2.5, debug@^3.2.6:
   version "3.2.6"
   resolved "https://registry.yarnpkg.com/debug/-/debug-3.2.6.tgz#e83d17de16d8a7efb7717edbe5fb10135eee629b"