It is shown, both analytically and by numerical simulations, that, in the presence of thermal ion kinetic effects, the beta induced Alfvén eigenmode (BAE)–shear Alfvén wave continuous spectrum can be discretized into radially trapped eigenstates known as kinetic BAE (KBAE). While thermal ion compressibility gives rise to finite BAE accumulation point frequency, the discretization occurs via the finite Larmor radius and finite orbit width effects. Simulations and analytical theories agree both qualitatively and quantitatively. Simulations also demonstrate that KBAE can be readily excited by the finite radial gradients of energetic particles.