A simple model for an electron in two dimensions interacting with an elastic distortion field shows interesting polaron-like behaviors. The model consists of a single tight-binding electron in a classical polarization field. The distortion potential ϕ and electron amplitude ψ evolve by coupled dynamical equations derived from a Lagrangian with cross term gϕ|ψ|². The equations of motion for ψ and ϕ are integrated together in time. For large enough g, the electron self-traps and a bound polaron-like object exists with time independent ϕ in the shape of a well and ψ a stationary state in the well. There is a critical value g_min below which the polaron well disappears. Spectral densities obtained by transforming double-time Green functions into [Formula: see text] show mass enhancement and lifetime broadening effects. The model, such as it is, can be extended easily to arbitrary, confined geometries in two or three dimensions.