In this study, we investigated the applicability of a Graphics Processing Unit (GPU)-based dynamic explicit finite element (FE) program for fast quasi-static deformation simulations of breasts, and proposed an optimisation-based method to estimate material parameters of in vivo breast tissues in the context of nonlinear hyperelastic models. Due to its high-speed execution, the GPU-based FE program was used as a forward solver in the optimisation process. A hybrid simulated annealing algorithm for global optimisation was employed to find the optimised material parameters by mininising the Euclidean distance between FE predicted displacements and estimated displacement from image registration at the selected landmark positions. The proposed method can be used for fast FE analyses of soft tissue deformations in medical image analyses and surgical simulations.