The present paper studies the critical condition for negative surface tension-driven circumferential wrinkling of soft cylinders based on the linearized Steigmann–Ogden model of surface elasticity. A simple negative surface tension-mode number relation is derived explicitly for arbitrary Poisson ratios of the cylinder and its surface layer and their shear modulus ratio, on which the critical surface residual strain and the associated mode number can be determined easily. For an incompressible solid cylinder with an incompressible thin surface layer, the critical values of surface residual strain and the mode number predicted by the present model are in good agreement with available numerical results based on the popular neo-Hooken nonlinear model for a wide range of material and geometrical parameters. In addition, the critical condition for circumferential wrinkling of the inner surface of a cylindrical hole within an infinite body is also derived. The present work addresses the key role of negative surface tension in circumferential wrinkling of soft cylinders and offers supporting evidence for the efficiency and accuracy of the linear Steigmann–Ogden model for the determination of the critical values for circumferential wrinkling.