At low light levels, detected photoevents can provide a physical source of random numbers. In turn, these optically generated random numbers can be used to construct Markov chains, which form the mathematical frame-work for many of the Monte Carlo procedures. In this paper a method for optically generating bivariate random deviates with a specified probability den-sity function and correlation coefficient is given. The optical implementations of two Monte Carlo procedures also are discussed. First, a method to calculate two-dimensional definite integrals is considered. Next, an optical method for solving systems of linear algebraic equations by the Von Neumann-U lam Monte Carlo procedure is given.