The mechanical characterization of new generations of materials such as polymer/carbon nanotube nanocomposites has always been challenging. In this research, the hardness and elastic modulus of single-walled carbon nanotube (SWCNT)-reinforced epoxy composites that have nonlinear elastic response were investigated using finite element analysis. A series of two-dimensional nanoindentation simulations were carried out to evaluate elastic modulus and hardness. The effects of volume percentages of the SWCNTs on the mechanical properties were evaluated. In addition, the effects of indenter geometry as well as friction coefficient on the response of nanoindentation were examined. The results indicated that the nanoindentation finite element models were able to simulate the loading-unloading responses of the epoxy/SWCNT nanocomposites. Nanoindentation investigations showed enhanced hardness and Young's modulus of nanocomposites by increasing the filler of SWCNTs as compared with pure epoxy. Future fabricated samples are expected to be promising materials for sensor and aircraft components. Furthermore, these simulated results show good agreement with experimental data from previous studies.