Cell spreading plays an important role in the modulation of physiological functions such as inflammation and cancer metastasis. The Brownian ratchet model and Bell's model have been used to simulate actin dynamics and bond kinetics for focal adhesion dynamics, respectively. In the present study, these models were modified and two additional subcellular mechanisms, integrin and myosin kinetics, were incoporated. An integrin recruitment function was introduced to determine the size of a focal adhesion associated with the substrate stiffness. The relationship between myosin concentration and the actin protrusion velocity was described by a first-order differential equation. Subcellular processes, including cell protrusion, focal adhesion formation, and stress fiber formation, were integrated into an axial-symmetric biophysical model, while inputs to the model were kinematic data from time-lapse experiments. Numerical simulations of the model using the Gillespie algorithm showed that dynamics of cell spreading can be well described by the model.