The application of Itô's formula induces some probabilistic representations of solutions of deterministic linear problems with boundary conditions of Dirichlet, Neumann, Fourier and mixed types. These representations are used to establish some easily implementable algorithms which compute an approximate solution by means of simulation of reflected random walks. They do not require selected configurations at the neighbourhood of the domain boundary, nor a discretization mesh. The associated simulation methods are obtained and applied to problems for each class of boundary conditions. Numerical experiments with distributed source in two- or three-dimensional geometries, and computational results with estimation of error, are reported. © 1997 by John Wiley & Sons, Ltd.