We develop an asymptotic solution for the axisymmetric squeeze flow of a viscoplastic Casson medium following the asymptotic technique suggested earlier by Balmforth and Craster (1999) and Frigaard and Ryan (2004). The no-slip and slip yield boundary conditions at the wall are considered. Depending on the ratio of two dimensionless parameters partial slip (stick-slip) or full slip at the wall (slip) are possible. We confirm numerically obtained solution, using Accelerated proximal gradient and Augmented Lagrangian methods.