The present work studies the problem of the flow field around the inlet section in the case of a plane slider bearing with upstream free surface. In order to determine the pressure head build-up, the inlet region of the bearing can be studied by considering a rigid plane sheet (pad) parallel to a plane wall (guide) which slides at a steady speed in a viscous incompressible fluid. The mathematical model described is based on the application of the theory of analytic functions. Through Dini's equation, which relates the real and the complex part of any analytic function, defined on the boundary of a domain, it is possible to determine the distribution of pressure on this boundary and the geometry of the free surface. In this way the problem is formally solved; however, it is difficult to obtain the solution because the thickness of the free surface is unknown. It would be possible to adopt an iterative method but the great difficulty associated with this method of solution induced the authors to follow a simplified technique. Through this study it was possible to determine the pressure build-up at the inlet; this quantity is the essential boundary condition to evaluate the actual load capacity of a slider bearing.