In accordance with some embodiments, systems, methods and media for simulating deformation of an elastic body are provided. In some embodiments, a method comprises: determining for each macroblock, a stiffness matrix Ki of a portion of a model of a non-linear elastic solid partitioned into cells; converting Ki into block form to include a submatrix KIiIi for nodes between internal cells of a first macroblock; determining at least a portion of KIiIi−1; receiving input corresponding to force applied to cells of the model; determining displacements of exterior nodes of the first macroblock using the input and the portion of KIiIi−1; determining displacements of interior nodes of the first macroblock using the input and the displacements of exterior nodes; determining updated positions of the cells based on the displacements of the exterior nodes; and, causing the model to be presented using the updated positions.