The Hamiltonian of a system ofNvortex lines moving in an incompressible fluid contained in a circular cylinder is given. The equilibrium state of vortices is constructed through minimization of the energy of the system with the constraints of constancy of number of vortices and their total angular momentum. One and only one assumption is usedthroughout this work, that pair correlation between vortices is neglected. In equilibrium, the system of vortices rotates uniformly with respect to the central axis of the cylinder. The fluid does not rotate as a solid body, only approaches solid rotation asN→∞. Continuous distribution functions of vortices are found for allN > 1. ForN = 1, the distribution is a delta function at the central axis of the cylinder. AsNincreases the distribution spreads out; in the limitN→∞, it becomes uniform throughout except for a thin layer of orderN−1/2approaching the wall where the density goes to zero rapidly but continuously and remains zero up to the wall. The vortex‐free region next to the wall has a thickness varying from1 − 1/√2forN = 2to1/√Nfor largeN.