The Monte Carlo method is inherently parallel and the extensive and rapid development in vector and parallel computers has resulted in renewed and increasing interest in this method. At the same time there has been an expansion in the application areas and the method is now widely used in many important areas of science including nuclear and semiconductor physics, statistical mechanics and heat and mass transfer. This work attempts to bridge the gap between theory and practice concentrating on modern algorithmic implementation on parallel architecture machines. Although a suitable text for final year or postgraduate mathematicians it is principally aimed at the applied scientists - only a small amount of mathematical knowledge is assumed and theorem proving is kept to a minimum, with the main focus being on parallel algorithm development often to applied industrial problems. Algorithms are developed both for MIMD machines with distributed memory and SIMD machines; a selection of programs are provided.