Abstract A terrace–step–kink model for epitaxial step flow growth of steps with no bonds along them is derived from kinetic arguments. The model is combined with an existing model for the steps that have strong bonding along them to describe steps of arbitrary orientation in terms of densities of adatoms, step adatoms and kinks. A planar steady-state solution for a simplified version of the model is constructed and analyzed. Different mass transport mechanisms are modeled that result in different far-from-equilibrium behavior, confirming that edge diffusion is the main factor stabilizing the steps during growth. Furthermore kinetic Wulff shapes are constructed from the calculated step velocities.