The problem of TM-wave scattering and radiation from a finite number of thick slits in a parallel plate waveguide is solved. The Fourier transform and the mode matching are used to obtain simultaneous equations for the field inside the slits. The simultaneous equations are solved 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 and useful for slotted-waveguide leaky-wave antenna applications.