  In this work, we derive exact self-consistent solutions to the gap equations
of the $\mathbb{C}P^{N-1}$ model on a finite interval with Dirichlet boundary
conditions in the large-$N$ approximation. The solution reproduce the confining
phase in the infinite system by taking the appropriate limit. We compute the
vacuum energy and the Casimir force and observe that the sign of the force is
always attractive.
