A novel 2D finite element (FE) associated with orthogonal finite functions (OFF, orthogonal splines) was developed for the ANSYS software and was tested early. The expansion of this method is presented here. The novel 3D FE, connected with 3D OFF is proposed for modeling and investigation of the stress-strain state of homogeneous and heterogeneous elastic bodies. The accuracy of the solutions obtained with this 3D FE is as high as for the classic ANSYS 3D FE. The developed 3D FE requires significantly less computational time; the winning of computational time increases with the amount of FE in a model.