Myosin is a major molecular force generator in the cell. The essential features of myosin interaction with actin filaments are understood. In the cell, the interactions of myosin with F-actin, substrate adhesions and other actin-associated proteins are less clear. We will borrow ideas from mathematical models of skeletal muscle to develop simple models for integrin focal adhesions, actin cross-linking proteins and non-muscle myosin-II. When these components are combined, a dynamical picture of the actin network emerges. In this talk, we will focus on the role of cell-substrate stiffness on the actin dynamics. Possible implications for mechanical sensing by cells are discussed.