The process of crystallization can be modeled by a population balance equation coupled with an energy balance equation. Such models are highly complex to study due to the infinite dimensional and nonlinear characteristics, especially when all the phenomena of nucleation, growth and breakage are considered. In the present paper, we have performed the stability analysis on a reduced order model obtained by the method of moments, which remains still highly complex. The considered model has been developed by the CEMAGREF and validated on experimental data. After computation, we get a scalar equation whose solutions correspond to the equilibrium points of the system. This equation is finally solved numerically for a concrete physical configuration of the crystallizer.We show that in most instances apart from the trivial equilibrium point, there is only one steady -state. Yet it is shown that for some particular parameter value combinations, multiple steady-states can be emphasized.