Elastic contact between a non-ideal Berkovich indenter and a half-space is investigated. The derived mathematical model of the contact allows for tangential displacements of the boundary points of the half-space. The tip of the blunted indenter is simulated as a smooth surface. The boundary element method is implemented in the model for numerical simulation of nanoindentation. The relative deviation function is introduced and calculated to quantify the influence of the tangential displacements on the load-displacement curves. A simple expression is derived for the impact of the tangential displacements on the values of the reduced Young's modulus determined due to nanoindentation studies. The refined model was successfully applied to simulate the experimental load-displacement curves gained by elastic nanoindentations of flat LiF and KCl samples. Such values of the indenter bluntness (the varying parameter) were found that the simulated load-displacement curves coincided with those of the experimental data at displacements higher than 7.5 nm. The model neglecting tangential displacements gives slightly differing values for the parameter of the indenter bluntness.