The multinomial probit model has long been used in transport applications; as the basis for mode- and routechoice in computing network flows, and in other choice contexts when estimating preference parameters. Over recent years, the use of probit in the choice modelling community has declined, with growing focus on mixed logit models. The theoretical appeal of the error structure of the probit model however remains, and recent work on composite marginal likelihood estimation (Bhat, 2010) has renewed interest in the probit model in the specific context of preference estimation. Whether using the probit model for estimating parameters or for evaluating choice proportions, computation of the choice probabilities presents a computational burden, given that they are based on multivariate normal integrals. In this paper we compare two analytical approximation methods for computing both the probit choice probabilities and their derivatives in terms of accuracy and computation efficiency. Here, we show that the “Mendell-Elston” approach outperforms the recently used “Solow-Joe” approach across a range of settings. Wider use of the “Mendell-Elston” in probit work, and implementation within a composite marginal likelihood estimator are thus promising areas for new developments. While the primary motivation for this paper is to help with the estimation and application of discrete choice models, there may be applications in other areas where the computation of multivariate normal integrals is needed.