A new second-order Saddlepoint Approximation (SA) method for structural reliability analysis is introduced in this paper. The Mean-value Second-order Saddlepoint Approximation (MVSOSA) is presented as an extension to the Mean-value First-order Saddlepoint Approximation (MVFOSA). The proposed method is based on a second-order Taylor expansion of the limit state function around the mean value of the input random variables and requires first and second-order sensitivity derivatives of the limit state function with respect to the random variables. If sensitivity analysis must be avoided because of computational cost, a quadrature integration approach, based on sparse grids is presented and linked to the saddlepoint approximation (SGSA – Sparse Grid Saddlepoint Approximation). The SGSA method is compared with the first and second-order SA methods in terms of accuracy and efficiency. The proposed MVSOSA and SGSA methods are demonstrated using multiple examples.