Summary: We study zero-pressure gas dynamics, which is a nonstrictly hyperbolic system of nonlinear conservation laws with delta-shock waves in solutions. By using generalized Rankine-Hugoniot relations to solve Riemann problem with two pieces of constant initial data, we obtain multidimensional planar delta-shock waves dependent upon a one-parametric family. Furthermore, we choose a unique entropy solution using the vanishing viscosity, and obtain a stability for delta-shocks.