This paper examines the linear response of a two-layer uniformly rotating ocean of infinite horizontal extent with a discontinuity in depth to a divergence-free transient wind stress. Initially the ocean is at rest and the wind stress is directed perpendicular to the escarpment. A rigid lid is employed to filter out the external double Kelvin wave and an analytic solution is derived, using transform techniques, for the forced internal double Kelvin wave which is trapped along the depth discontinuity. Parameter values are chosen which most accurately model the Mendocino escarpment oriented almost zonally off the northern California coast. Soon after the wind stress is applied a single large wave is generated in the neighborhood of the wind stress curl origin. The wave has a maximum amplitude of 3 m, a phase speed of approximately 2.2 km day–1 and a wavelength in the order of 200 km. Furthermore the forced double Kelvin wave is found to exhibit a 6 day oscillation which is independent of the e-folding time scale of the wind stress. At any fixed location along the escarpment the solution also displays amplitude modulation. An investigation of how sensitive the solutions are to the upper layer depth and stratification is presented. A brief discussion of the response produced by a time-periodic spatially independent wind stress directed parallel to the escarpment and suddenly applied to a quiescent ocean, is also presented. It is suggested that double Kelvin waves may perhaps be detected from deep-sea buoy measurements.