In the present study, we examine the ability of FE models with several constitutive relations (elastic, elastic-plastic, linear and nonlinear viscoelastic and their combination) to reproduce the response of a C-S-H phase of hardened cement paste measured in a cyclic nanoindentation experiment. It is found that the linear viscoelastic model, which fits very well a single loading-dwell-unloading cycle, does not properly describe the consequent cycles. The best results are obtained with a combined nonlinear viscolelastic and plastic model. A parametric study is performed to identify the model parameters. The model is then employed to analyze various aspects of the experiments, such as, the size of indent influence zone, the distribution of residual stresses and strains, the effect of indenter shape simplification (pyramidal to axisymmetric cone), the effect of material inhomogeneity in the indent vicinity, and others.