Conformal arrays are popular antennas for aircraft, spacecraft, and land vehicle platforms due to their inherent low weight, drag, and observables. However, to date there has been a dearth of rigorous analytical or numerical solutions to aid the designer. In fact, it has been common practice to use limited measurements and planar approximations in designing such nonplanar antennas. We extend the finite element-boundary integral method to scattering by cavity-backed structures in an infinite, metallic cylinder. In particular, we discuss the formulation specifics, such as weight functions, dyadic Green's function, implementation details, and particular difficulties inherent to cylindrical structures. Special care is taken to ensure that the resulting computer program has low memory demand and minimal computational requirements. Scattering results are presented and validated as much as possible. >