In this paper,  we are concerned with  two-dimensional centered expansion fans in the Guderley Mach reflection configurations for pseudo-steady flow in gas dynamics. In order to construct such a centered expansion fan, a centered wave problem is set up. Existence of global classical solution to the centered wave problem for two-dimensional isentropic irrotational pseudo-steady Euler equations is obtained constructively. The techniques used here can be useful for constructing centered wave flow patterns of other flow problems and for constructing global classical solutions to centered wave problems for some other types of quasilinear hyperbolic syste.