Real time computation of soft tissue deformation is important for the use of augmented reality devices and for providing haptic feedback during operation or surgeon training. This requires algorithms that are fast, accurate and can handle material nonlinearities and large deformations. A set of such algorithms is presented in this paper, starting with the finite element formulation and the integration scheme used and addressing common problems such as hourglass control and locking. The computation examples presented prove that by using these algorithms, real time computations become possible without sacrificing the accuracy of the results. For a brain model having more than 7000 degrees of freedom, we computed the reaction forces due to indentation with frequency of around 1000 Hz using a standard dual core PC. Similarly, we conducted simulation of brain shift using a model with more than 50,000 degrees of freedom in less than one minute. The speed benefits of our models result from combining the Total Lagrangian formulation with explicit time integration and low order finite elements.