The nanoindentation loading response of elastoplastic materials was simulated by the finite element method (FEM). The influence of the Young's modulus E, yield stress σ, strain hardening exponent n and Poisson's ratio ν on the loading response was investigated. Based on an equivalent model, an equation with physical meaning was proposed to quantitatively describe the influence. The calculations agree well with the FEM simulations and experimental results in literature. Comparisons with the predictions using equations in the literature also show the reliability of the proposed equation. The investigations show that the loading curvature C increases with increasing E, σ, n and ν. The increase rates of C with E, σ, n and ν are different for their different influences on the flow stress after yielding. It is also found that the influence of one of the four mechanical parameters on C can be affected by the other mechanical parameters.