Friction drilling uses a rotating conical tool to penetrate the workpiece and create a bushing in a single step without generating chips. This research investigates the three-dimensional (3D) finite element modeling (FEM) of large plastic strain and high-temperature work-material deformation in friction drilling. The explicit FEM code with temperature-dependent mechanical and thermal properties, as well as the adaptive meshing, element deletion, and mass scaling three FEM techniques necessary to enable the convergence of solution, is applied. An inverse method to match the measured and modeling thrust force determines a coefficient of friction of 0.7 in this study. The model is validated by comparing the thrust force, torque, and temperature to experimental measurements with reasonable accuracy. The FEM results show that the peak temperature of the workpiece approaches the work-material solidus temperature. Distributions of plastic strain, temperature, stress, and deformation demonstrate the thermomechanical behavior of the workpiece and advantages of 3D FEM to study of work-material deformation in friction drilling.