diff --git a/tests/cypress/integration/issue_1391_delete_point.js b/tests/cypress/integration/issue_1391_delete_point.js
new file mode 100644
index 00000000..d174a6e9
--- /dev/null
+++ b/tests/cypress/integration/issue_1391_delete_point.js
@@ -0,0 +1,82 @@
+/*
+ * Copyright (C) 2020 Intel Corporation
+ *
+ * SPDX-License-Identifier: MIT
+ */
+
+/// <reference types="cypress" />
+
+context('When delete a point, the required point is deleted.', () => {
+
+    const issueId = '1391'
+    const labelName = `Issue ${issueId}`
+    const taskName = `New annotation task for ${labelName}`
+    const attrName = `Attr for ${labelName}`
+    const textDefaultValue = 'Some default value for type Text'
+    const image = `image_${issueId}.png`
+    const width = 800
+    const height = 800
+    const posX = 10
+    const posY = 10
+    const color = 'white'
+    let pointsСoordinatesBeforeDeletePoint = []
+    let pointsСoordinatesAfterDeletePoint = []
+
+    before(() => {
+        cy.visit('auth/login')
+        cy.login()
+        cy.imageGenerator('cypress/fixtures', image, width, height, color, posX, posY, labelName)
+        cy.createAnnotationTask(taskName, labelName, attrName, textDefaultValue, image)
+        cy.openTaskJob(taskName)
+    })
+
+    describe(`Testing issue "${issueId}"`, () => {
+        it('Crearte polyline', () => {
+            cy.createPolyline('Shape', [
+                {x: 309, y: 250},
+                {x: 309, y: 350},
+                {x: 309, y: 450}
+              ])
+            cy.get('#cvat-objects-sidebar-state-item-1')
+            .should('contain', '1').and('contain', 'POLYLINE SHAPE')
+        })
+        it('Get points coordinates from created polyline', () => {
+            cy.get('#cvat_canvas_shape_1').should('have.prop', 'animatedPoints')
+            .then(($pointsСoordinates) => {
+                for (let i of $pointsСoordinates) {
+                    pointsСoordinatesBeforeDeletePoint.push(`${i.x}, ${i.y}`)
+                }
+            })
+        })
+        it('Remove the second point from created polyline', () => {
+            cy.get('#cvat_canvas_shape_1')
+            .trigger('mousemove', {force: true})
+            .trigger('mouseover', {force: true})
+            cy.get('.svg_select_points').then(points => {
+                cy.get(points).eq(0).then(point1 => {
+                    cy.get(point1)
+                    .rightclick()
+                })
+                cy.get(points).eq(1).then(point2 => {
+                    cy.get(point2)
+                    .rightclick({force: true})
+                })
+                cy.contains('Delete point')
+                .click()
+            })
+        })
+        it('Get points coordinates from turned out polyline', () => {
+            cy.get('#cvat_canvas_shape_1').should('have.prop', 'animatedPoints')
+            .then(($pointsСoordinates) => {
+                for (let i of $pointsСoordinates) {
+                    pointsСoordinatesAfterDeletePoint.push(`${i.x}, ${i.y}`)
+                }
+            })
+        })
+        it('Coordinate of second point before delete not in coordinates array after delete', () => {
+            cy.get(pointsСoordinatesBeforeDeletePoint).then(point => {
+                cy.expect(pointsСoordinatesAfterDeletePoint).not.contain(point[1])
+            })
+        })
+    })
+})
diff --git a/tests/cypress/support/commands.js b/tests/cypress/support/commands.js
index 84f85708..20eb9b60 100644
--- a/tests/cypress/support/commands.js
+++ b/tests/cypress/support/commands.js
@@ -210,3 +210,22 @@ Cypress.Commands.add('updateAttributes', (additionalAttrName, typeAttribute, add
     cy.get('.ant-select-dropdown').last().contains(typeAttribute).click()
     cy.get('[placeholder="Default value"]').first().type(additionalValue)
 })
+
+Cypress.Commands.add('createPolyline', (mode,
+                                        pointsMap) => {
+    cy.get('.cvat-draw-polyline-control').click()
+    cy.contains('Draw new polyline')
+    .parents('.cvat-draw-shape-popover-content')
+    .within(() => {
+        cy.get('button')
+        .contains(mode)
+        .click({force: true})
+    })
+    pointsMap.forEach(element => {
+        cy.get('.cvat-canvas-container')
+        .click(element.x, element.y)
+    })
+    cy.get('.cvat-canvas-container')
+    .trigger('keydown', {key: 'n'})
+    .trigger('keyup', {key: 'n'})
+})