Solid and elastic contact problems have been thoroughly investigated before. The most recent efforts incorporate the use of the Lennard-Jones (LJ) potential to describe the intersurface forces that are present and substantial in micro-sized contact problems. But little work has been done on viscoelastic contact problems. Hence, there is a need to investigate the behaviour of a viscoelastic contact under the LJ interaction. This paper aims to investigate the deformation of an axisymmetric viscoelastic tip that is either pushed onto or pulled from a flat rigid surface. From existing elastic models, a mathematical model was developed to describe the contact problem in a viscoelastic context. This newly developed was solved via numerical means. The result is a model that readily accepts measureable physical properties and gives out the deformation of a viscoelastic tip.