Transverse stimulated Raman scattering (TSRS) in potassium dihydrogen phosphate (KDP) and deuterated potassium dihydrogen phosphate (DKDP) plates for large-aperture, inertial confinement fusion (ICF)-class laser systems is a well-recognized limitation giving rise to parasitic energy conversion and laser-induced damage. The onset of TSRS is manifested in plates exposed to the ultraviolet section of the beam. TSRS amplification is a coherent process that grows exponentially and is distributed nonuniformly in the crystal and at the crystal surfaces. To understand the growth and spatial distribution of TSRS energy in various configurations, a modeling approach has been developed to simulate the operational conditions relevant to ICF-class laser systems. Specific aspects explored in this work include (i) the behavior of TSRS in large-aperture crystal plates suitable for third-harmonic generation and use as wave plates for polarization control in current-generation ICF-class laser system configurations; (ii) methods, and their limitations, of TSRS suppression and (iii) optimal geometries to guide future designs.