The paper develops a theory of the growth of a polydisperse ensemble of anisotropic particles in a supersaturated solution. An ellipsoidal coordinate system is used to describe the shape of growing particles. An integrodifferential system of mass balance and Fokker-Planck equations is formulated and solved analytically. Asymptotic solutions for the crystal volume distribution function and solution supersaturation are constructed. © 2023 AIP Publishing LLC.