We extend known saddlepoint tail probability approximations to multivariate cases, including multivariate conditional cases. Our first approximation applies to both continuous and lattice variables, and requires the existence of a cumulant generating function. The method is applied to some examples, including a real data set from a case-control study ofendometrial cancer. The method contains less terms, is easier to implement than existing methods, and shows an accuracy comparable to that of existing methods. The drawback of the first method is thatthe coefficient for the main term is not 1, and therefore it may be hard to show the reflexivity property which in general does not hold, because the route of path of the integral used in the saddlepoint method has to have positive real part. Our second method uses a different approach for the main term. We show that in the bivariate case, the reflexivity property holds. We applies the method to a three dimensional example, and our method demonstrates better accuracy than the normal approximation.