This paper presents an effective three-dimensional (3D) nonlinear explicit dynamic meshfree algorithm for the simulation of soft tissue mechanical responses. In the algorithm soft tissues are considered to be hyperelastic and nearly incompressible materials. The algorithm is based on the element-free Galerkin (EFG) method using total Lagrangian formulation and moving least square (MLS) approximation. This approximation uses a relatively large number of nodes for shape functions creation, which can significantly delay mesh distortion in large deformation computations. Essential boundary conditions are imposed exactly by coupling MLS shape functions with a finite element (FE) interpolation in the close region of essential boundary. Although volumetric integration is not exact, the large support domains of the MLS shape functions alleviate some of the key weaknesses of FE methods such as hour-glassing and volumetric locking. Explicit integration is performed in time domain, using a recently proposed method to calculate the critical time step. Verification against the results obtained using the established nonlinear finite element procedures available in the ABAQUS code confirms the accuracy of the presented meshfree algorithm. Application of the algorithm in modeling of the brain indentation indicates its ability to facilitate robust and accurate prediction of the organ responses subjected to large localized deformations consistent with the loading due to surgery. © 2013 Elsevier Ltd. All rights reserved.