The problem of TE-wave scattering and radiation from a finite number of thick slits in a parallel-plate waveguide is solved. The Fourier transform is used to express the scattered field in the spectral domain. The boundary conditions are enforced to obtain a series solution which is amenable to numerical computation. The numerical computations are performed to illustrate the behaviors of scattering, transmission, and reflection in terms of incident angle, slit size and operating frequency. The presented solution is computationally very efficient so that it is useful for slotted-waveguide leaky-wave antenna applications.