The current study examined the effect of nanoparticles shapes on magnetohydrodynamics (MHD), Casson hybrid nanofluids flow, and heat transfer over a moving vertical plate with convective boundary condition. In this study, a base fluid (water) was infused with silver (Ag) and titanium oxide (TiO2). Similarity transformation techniques are used to convert the partial differential equations of Casson hybrid nanofluids to an ordinary differential equation, which are then solved numerically by applying the implicit finite difference, Keller box method. The velocity and temperature profiles, skin friction, and Nusselt number of Casson hybrid nanofluids were graphically illustrated and numerically tabulated. The results indicate that platelets have the highest velocity and temperature profiles, followed by cylindrical, bricks, and spherical nanoparticles. It was discovered that as the parameters aligned angle of the magnetic field, magnetic field interaction, mixed convection, Casson hybrid nanofluids, and Biot number increase, the velocity increases while the temperature decreases. As the volume fractions of Ag and TiO2 nanoparticles increase, the velocity decreases while the temperature increases. Except for the Casson hybrid nanofluids parameter, the skin friction and Nusselt number increase as the aligned magnetic angle, magnetic field interaction, mixed convection, volume fraction of Ag and TiO2 nanoparticles, and Biot number is increased. For all parameters, the plate with the condition moving with the flow has the highest velocity and Nusselt number, followed by the static and moving against the flow plates. When it comes to temperature and skin friction, the plate that is moving against the flow has the highest temperature, followed by the plate that is static and moving along the plate. The findings of this work will contribute to the corpus of knowledge in mathematics by providing fresh information for mathematicians interested in future research on Casson hybrid nanofluids.