Cell motility is central to a variety of fundamental processes ranging from cancer metastasis to immune responses, but it is still poorly understood in realistic native environments. Previous theoretical work has tended to focus on intracellular mechanisms or on small pieces of interaction with the environment. In this article, we present a simulation which accounts for mesenchymal movement in a 3D environment with explicit collagen fibers and show that this representation highlights the importance of both the concentration and alignment of fibers. We show good agreement with experimental results regarding cell motility and persistence in 3D environments and predict a specific effect on average instantaneous cell speed and persistence. Importantly, we show that a significant part of persistence in 3D is directly dependent on the physical environment, instead of indirectly dependent on the environment through the biochemical feedback that occurs in cell motility. Thus, new models of motility in three dimensions will need to account for the effects of explicit individual fibers on cells. This model can also be used to analyze cellular persistence in both mesenchymal and nonmesenchymal motility in complex three-dimensional environments to provide insights into mechanisms of cell motion seen in various cancer cell types in vivo.