A continuum model for sand production is developed by considering coupling of fluid flow and rate-sensitive plastic flow of granular matrix. Initial granular matrix yielding is reached as a result of wellbore fluid pressure reduction (drawdown) below some critical level. The model provides a physical mechanism of yielding front propagation away from the wellbore as the process of sand production continues. Mass balance analysis leads to a relation between cumulative sand production and the current yielding front location. Different regimes of sand production, limited and unstable, are considered. Fluid production enhancement because of simultaneous sand production turns out to be dependent not only on instantaneous sand flux, but also on the current radius of the yielded zone around wellbore, that is, the history of sand production for the well.