We develop an asymptotic solution for the axisymmetric squeeze flow of a viscoplastic medium. The standard lubrication-style expansions of the problem predict a plug speed which varies slowly in the principal flow direction. This variation implies that the plug region cannot be truly unyielded. Our solution shows that this region is a pseudo-plug region in which the leading order equation predicts a plug, but really it is weakly yielded at a higher order. We follow the asymptotic technique suggested earlier by Balmforth and Craster (1999) and Frigaard and Ryan (2004). This method involves no relaxation of the exact Bingham model. The analytical expression for the squeeze force is in good agreement with previous numerical results. In the second part of the paper, the axisymmetric squeeze flow of a Bingham fluid with slip yield boundary condition at the wall is considered. We provide an asymptotic solution for this type of flow. Depending on the ratio of two dimensionless parameters partial slip (stick-slip) or full slip at the wall (slip) are possible.