Monte Carlo algorithms for solving boundary value problems for elliptic differential equations are studied. In particular two Monte Carlo numerical algorithms are considered. The first one is so-called grid-walk (GW) algorithm, white the second one is grid-free (GF) algorithm. The first algorithm uses a discretisation of the problem on a mesh and solves the linear algebraic system, which approximates the original problem. The second algorithm uses an integral representation for the problem. For the studied algorithms a new data parallel approach is applied. It is shown that the numerical solution of partial differential equations, can be efficiently addressed in a functional language. These algorithms have been implemented in parallel on a MIMD-machine with distributed memory. Experimental results that they behave well and that due to small amount of communication a linear speedup is possible.