Traditional slip-line field theory considers steady-state pressure distributions. This work examines the evolution of pressure at yield. We show that, for a two phase material in plane strain at the point of plastic yield of the main constituent, pressure develops according to dissipative wave mechanics. The pressure wave equations are examined in more detail for the special case of radially symmetric plane strain, and for Von Mises and Drucker-Prager yield envelopes. The positions of pressure troughs are compared to the separation of slip-lines formed during the expansion by internal pressurisation of a cylinder of mild steel.