We developed analytical solutions to the wind set-down and the wind set-down relaxation problems. The response of the ocean to the wind blowing over a long-narrow and linearly sloping shallow basin is referred to as wind set-down. The shoreline exhibits oscillatory behavior when the wind calms down and the resulting problem is referred to as wind set-down relaxation. We use an existing hodograph-type transformation that was introduced to solve the nonlinear shallow-water wave equations analytically for long wave propagation and obtain an explicit-transform analytical solution for wind set-down. For the wind set-down relaxation, the nonlinear shallow-water wave equations are solved analytically as an initial-boundary value problem, with forced initial data derived from our wind set-down solution.