"Mathematical methods are being developed for calculations in fluid dynamics. The work to date on the Mach reflection calculation is summarized. In the flow, there are two curved shocks, a slip surface, a plane shock, and rigid walls. The desired solution of the fluid-dynamics equations is stationary in similarity variables; approximate initial data are therefore assumed, with the expectation that the flow will settle down to the desired one asymptotically. The Eulerian equations for the smooth parts of the flow are coupled to the jump and boundary conditions on the various surfaces. Two-dimensional fitting procedures were devised to apply the jump and boundary conditions. All parts of the code now appear to operate satisfactorily except for the treatment of the slip surface, which showed instabilities after about 50-70 cycles. The main problem was temporarily discontinued, in order to concentrate on the slip surface. A simplified problem of a nearly plane slip surface between parallel walls and with periodicity conditions along the surface is described. This problem uses all the machinery of the main code except for the parts having to do with the shocks, and it has additional subroutines for computing an analytic solution based on the linearized theory of …