If you are dealing with a low dimension such as the trivariate normal distribution, the task is simple. A good scientific software must have a reliable built-in three-dimensional quadrature routine. For example, Maple 8 has a quick and accurate routine called Tripleint (I am NOT affiliated with Maple in any way !). All you have to do is enter the trivariate normal density function and use it as an input to the Tripleint routine to get the cumulative function.As far as paper references are concerned, you could check out the classical paper by R.Geske and H.E.Johnson ("The American Put Option Valued Analytically", The Journal of Finance, Vol. XXXIX, n°5, December 1984) : they find clever tricks to reduce the dimensionality of the problem (p.1520). From an applied mathematician standpoint, the best overview is probably the one done by A.Genz, already mentioned in this thread.In an option pricing context, the problem is also tackled by T.Guillaume in "Analytical Valuation of Options on Joint Minima and Maxima" (2001), Applied Mathematical Finance, 8, 209-233, as well as in a forthcoming paper in Review of Derivatives Research.