The theory of linear and stimulated free‐electron lasers using the Smith‐Purcell effect is presented. These lasers depend upon the resonant interaction of an electron beam with the longitudinal field of a surface‐harmonic wave on a diffraction grating. Detailed design criteria for the linear Smith‐Purcell‐effect laser are determined. Numerical estimates show that infrared lasers are feasible at beam currents smaller than 1 A and that single‐mode operation may be achieved. Saturation estimates determine the power output in the range 102W. An expression for the gain of the stimulated Smith‐Purcell laser is derived. The frequency up‐conversion factor for the stimulated interaction may be very large. Its possible use as a soft x‐ray laser is limited by the available intensity of the pump wave.