Quantitative measurements of viscoelastic material properties of soft materials such as hydrogels and tissues pose several challenges. Sample geometry (shapes, sizes and surfaces), the method of testing (compression, torsion or indentation), and the rate of loading all affect the measurements made on these materials. Additionally, hydrated media are commonly assumed to be single-phase, homogeneous materials, when in reality they are composed of a solid matrix with a fluid phase that fills the interstitial voids. In this study, spherical indentation and parallel plate shear tests are used to characterize the behavior gelatin hydrogels. The time-dependent shear moduli estimated from indentation tests (load relaxation and quasi-static) and shear stress relaxation tests are inherently different. However, the relaxed modulus estimated from all three tests agree well (within 12%) for a range of gelatin hydrogel concentrations similar in stiffness to soft tissues. Finite element analysis (FEA) using a biphasic poroviscoelastic model is used to predict the experimentally observed behavior as well as probe the solid-fluid interactions within the hydrogel. FEA is also used in parametric studies exploring the effects of geometry (height and width) of hydrogels, similar to those encountered in mechanobiology experiments of 3D cell cultures, to establish protocols that enable reliable measurements of material properties.