A stochastic algorithm for high-dimensional integrals over unbounded regions with Gaussian weight. The paper presents an algorithm that uses stochastic spherical-radial rules for the numerical computation of multiple integrals. These rules have higher accuracy and better convergence properties than simple Monte Carlo methods. The Fortran implemetation of the algorithm (RANRTH) is discussed, too. An example from a computational finance application is included (n variables, n>100).