Ductile fracture of metals involves nucleation, growth, and coalescence of voids. Starting from the pioneering work of Gurson, there have been constitutive models developed from first principles to characterize the growth and coalescence of voids. A new theory of multisurface plasticity accounts for homogeneous (or void growth) and multiple inhomogeneous yielding (or coalescence-like) mechanisms is presented. The theory is similar to the continuum crystal plasticity theory; inhomogeneous yielding systems are akin to slip systems. However, due to the well-known drawbacks of the rate-independent implementation of crystal-plasticity-like models, a formulation for rate-dependent solids is presented here. The elastic-viscoplastic constitutive relations are defined based on Norton’s law and plastic potentials for homogeneous and inhomogeneous yieldings. Finally, the developed rate-dependent formulation is generalized to be adopted for any improved future models.