Asbtract:  High-dimensional analytically intractable integrals are a pervasive problem in Bayesian inference. Monte Carlo methods can be used in the analysis of models where such problems arise. However, for large datasets or complex models such methods become computationally burdensome and it may become desirable to seek alternatives. Popular deterministic alternatives include variational Bayes and Laplace's method. However, variational Bayes only performs well under particular conjugacy and independence assumptions and Laplace's method only works well when the posterior is nearly normal in shape. In this talk I introduce the skew-normal variational approximation which minimises the Kullback-Leibler distance between a posterior density and a multivariate skew-normal density. The resulting approximation often simplifies calculations to the maximisation of a sum of univariate integrals which may be handled using a combination of standard optimisation and quadrature techniques. It is shown for a number of examples that the approach is more accurate than variational Bayes and Laplace's method whilst remaining faster than standard Monte Carlo methods.