The study of indentation responses of rate-dependent (viscoplastic or creeping) solids has generally focused on the relationship between indentation hardness and an effective strain rate, which can be defined from a similarity transformation of the governing equations. The strain rate sensitivity exponent can be determined from the slope of a log-log plot of the hardness versus effective strain rate, while determining other constitutive parameters requires a knowledge of the relationship between contact size, shape, and indentation depth. In this work, finite element simulations have shown that the effects of non-axisymmetric contact and crystallography are generally negligible. Theoretical predictions agree well with real nanoindentation measurements on amorphous selenium when tested above glass transition temperature, but deviate quite significantly for experiments on high-purity indium, coarse-grained aluminum, and nanocrystalline nickel. Such a discrepancy is likely to result from the transient creep behavior.