A derivation is given for the electromagnetic field produced by an arbitrary slot cut in the surface of an elliptic cylinder of perfect conductivity and infinite length. The electric field tangential to the slot is assumed to be a prescribed function. The integrals in the formal solution are evaluated by the saddle point method for the far zone fields which when specialized to thin transverse or axial slots agree with known results. As illustrative examples, patterns of thin axial and transverse slots on a strip are computed.