We present numerical solutions of a two-dimensional inviscid Burgers equation which provides an asymptotic description of the Mach reflection of weak shocks. In our numerical solutions, the incident, reflected, and Mach shocks meet at a triple point, and there is a supersonic patch behind the triple point, as proposed by Guderley for steady weak-shock reflection. A theoretical analysis indicates that there is an expansion fan at the triple point, in addition to the three shocks. The supersonic patch is extremely small, and this work is the first time it has been resolved.