The theory of resistive evolution of plasmas is extended to include plasmas with imperfect magnetic surfaces, that is, plasmas having magnetic field lines that wander stochastically. In resistive evolution theory the plasma is assumed to be always in mechanical equilibrium and the evolution occurs by allowing the magnetic flux constraints determining the equilibrium to change, which happens on a resistive time scale. In this paper a formalism is created to describe magnetic field line structure in a general way in order to evaluate the field line integrals that are the magnetic flux constraints. The equations expressing evolution of these flux constraints, along with the plasma mechanical equilibrium equations, are a mathematical model that can be solved to determine the evolution of the plasma. An immediate result of this model is that, for plasmas with stochastic magnetic field lines, the current density has a filamentary structure, giving a self‐consistent source of the stochasticity. A simple two‐field‐line model of the reversed field pinch is discussed.