Abstract Recent in situ observations from the Parker Solar Probe (PSP) mission in the inner heliosphere near perihelia show evidence of ion beams, temperature anisotropies, and kinetic wave activity, which are likely associated with kinetic heating and acceleration processes of the solar wind. In particular, the proton beams were detected by PSP/Solar Probe Analyzers-Ion (SPAN-I) and related magnetic fluctuation spectra associated with ion-scale waves were observed by the FIELDS instrument. We present the ion velocity distribution functions (VDFs) from SPAN-I and the results of 2.5D and 3D hybrid-particle-in-cell models of proton and α particle super-Alfvénic beams that drive ion kinetic instabilities and waves in the inner heliospheric solar wind. We model the evolution of the ion VDFs with beams, and obtain the ion relative drifts speeds, and ion temperature anisotropies for solar wind conditions near PSP perihelia. We calculate the partition of energies between the particles (ions) along and perpendicular and parallel to the magnetic field, as well as the evolution of magnetic energy, and compare to observationally deduced values. We conclude that the ion beam driven kinetic instabilities in the solar wind plasma near perihelia are important components in the cascade of energy from fluid to kinetic scales, an important component in the solar wind plasma heating process.