Cell motility is important for many developmental and physiological processes. Motility arises from interactions between physical forces at the cell surface membrane and the biochemical reactions that control the actin cytoskeleton. To computationally analyze how these factors interact, we built a three-dimensional stochastic model of the experimentally observed isotropic spreading phase of mammalian fibroblasts. The multiscale model is composed at the microscopic levels of three actin filament remodeling reactions that occur stochastically in space and time, and these reactions are regulated by the membrane forces due to membrane surface resistance (load) and bending energy. The macroscopic output of the model (isotropic spreading of the whole cell) occurs due to the movement of the leading edge, resulting solely from membrane force-constrained biochemical reactions. Numerical simulations indicate that our model qualitatively captures the experimentally observed isotropic cell-spreading behavior. The model predicts that increasing the capping protein concentration will lead to a proportional decrease in the spread radius of the cell. This prediction was experimentally confirmed with the use of Cytochalasin D, which caps growing actin filaments. Similarly, the predicted effect of actin monomer concentration was experimentally verified by using Latrunculin A. Parameter variation analyses indicate that membrane physical forces control cell shape during spreading, whereas the biochemical reactions underlying actin cytoskeleton dynamics control cell size (i.e., the rate of spreading). Thus, during cell spreading, a balance between the biochemical and biophysical properties determines the cell size and shape. These mechanistic insights can provide a format for understanding how force and chemical signals together modulate cellular regulatory networks to control cell motility.