In endoscopic liver surgeries, biomechanical models can provide information for the surgery guidance systems where elastic parameters and boundary conditions are important to improve computational accuracy. However accurate elastic parameters and boundary conditions are challenging to estimate. In this paper, a novel inverse method was proposed to estimate the friction boundary conditions and unknown Young's modulus of the heterogeneous tissue under local displacement observation in endoscopic liver surgeries scenarios. The friction boundary conditions and tissue Young's modulus were estimated by constructing the iterative parameter vector using the observed displacement information. In addition, the soft tissue variable boundary conditions were modeled to consider the changing of boundary conditions due to tissue deformation during the operation. The simulation and physical experiments were conducted and the results showed that the estimation results of boundary conditions and Young's modulus agreed well with expected values.