This work studies numerically the development of adiabatic shear banding (ASB) during high strain-rate compression of AISI 1045 steel. Plane strain and cylindrical axisymmetric compressions are simulated in LS-DYNA, considering rectangular and cylindrical steel samples, respectively. Also, a parametric analysis in height-to-base ratio is conducted in order to evaluate the effect of geometry and dimensional ratio of the sample on ASB formation. Doubly structural-thermal-damage coupled finite element models are developed for the numerical simulations, implementing the thermo-viscoplastic Modified Johnson–Cook constitutive relation and damage criterion, while further damage-equivalent stress and strain fields are introduced for the damage coupling. The simulations revealed that plane strain compression promotes more ASB formation, providing lower critical strain for ASB initiation and wider and stronger ASBs compared with axisymmetric compression. Further, X-shaped ASBs initially form during plane strain compression, while as deformation increases, they transform into S-shaped ASBs in contrast to axisymmetric compression, where parabolic ASBs are developed. Also, a lower height-to-base ratio leads to greater ASB propensity, reducing critical strain in axisymmetric compression. Finally, thermal softening is found to precede damage softening and dominate the ASB genesis and its early evolution, while in contrast damage softening drives later ASB evolution and its transition to fracture.