Particles precipitated during aging treatments often have non-spherical shapes, e.g., needles or plates, while in the classical Kampmann–Wagner Numerical (KWN) precipitation model, it is assumed that the particles are of spherical shape. This model is here generalized resulting in two correction factors accounting for the effects induced by the particles’ non-spherical shape on their growth kinetics. The first one is for the correction of the growth rate. It is derived from the approximate solution of the diffusion problem on spheroidal coordinate and verified by the three-dimensional numerical solutions for cuboid particles. The second factor is for the energetic correction due to the particle surface curvature. It is derived from chemical potential equality (or Gibbs energy minimization principle) at equilibrium for non-spherical particles and provides a correction factor for the Gibbs–Thomson effect. In the accompanying paper, the two correction factors are implemented into a multi-component KWN modeling framework, and the resulting improvements on the model’s predictive power are demonstrated.