The structural integrity of cancellous bone, which is essential to skeletal load-bearing capacity, is governed chiefly by apparent density, trabecular architecture, and tissue material properties. Metabolic bone disorders such as osteoporosis can affect each of these factors separately, resulting in compromised load-bearing function. While the impact of apparent density and architecture on bone mechanical behavior has been well-documented, much less is known about the influence of tissue material properties, particularly in osteoporotic bone. The goal of the present study is to isolate the influence of tissue material properties on the pre-yield mechanical response of normal and osteoporotic cancellous bone to uniaxial compression using finite element (FE) models derived from 3D micro-computed tomography images. Both average tissue material properties and the degree of tissue material heterogeneity vary between individuals. Therefore, three sets of FE models were created to study the relative importance of these two factors: 1) models with material homogeneity within and between subjects, 2) models with material homogeneity within subjects only, and 3) models with material heterogeneity within and between subjects. The results of finite element analyses were compared to data gathered from physical testing with matched conditions. For normal bone, incorporating material heterogeneity within and between subjects had no significant effect on model performance. For osteoporotic bone, incorporating material heterogeneity within subjects did not affect model performance, but models that incorporated subject-specific average material properties were significantly more accurate in replicating the results of physical testing. We conclude that, while the influence of bone apparent density and trabecular architecture on apparent stiffness are dominant in healthy bone, average material properties also play a role in osteoporotic bone. Osteoporosis is diagnosed based on apparent density alone, so our findings suggest a need to consider other patient-specific differences that may affect average tissue material properties, such a bone remodeling rate, in clinical assessments of osteoporotic bone structural integrity.