This paper presents a solution to the elasto-hydrodynamic problem of normal approach of two cylindrical bodies separated by a lubricating film. Analytic solutions are found for the special cases of constant viscosity and rigid material and also for pressure-dependent viscosity. The more general case accounting for elastic deformation of the bodies with constant or pressure dependent viscosity was solved by using an iterative numerical process with the help of an electronic computer. It is found that a very high pressure may be developed in the lubricant film at a finite separation of the cylinders. As the film thickness is further reduced, the value of the maximum pressure decreases and as the film thickness approaches zero, the pressure distribution converges to the Hertzian dry contact form. For a given load applied to the cylinders, the value of the maximum pressure reached depends to a large extent upon the value of the parameter $\alpha E$, i.e. the product of the pressure coefficient of viscosity and the equivalent Young's modulus of the elastic system. Also, once the pressure has reached a sufficiently high value it becomes extremely sensitive to an increase in load; a small increase in load will produce a large increase in maximum pressure. A number of experiments were performed in order to check some of the theoretical predictions made. In these experiments a loaded steel ball was allowed to approach the polished surface of various materials whose surfaces were covered by a lubricant film, and the plastic deformations produced in the surface were then measured. These tests showed clearly the influence of the lubricant in that in every case the depth of the impressions with lubricant was significantly larger than the corresponding ones produced under Hertzian, dry contact impacts. The experimental results indicate a correlation between maximum pressure and the value of $\alpha E$ and its sensitivity to increase in load at high pressure as predicted by the theory.