Gauge theory with massless fermions on a cylinder [= (1 + 1)-dimensional spacetime with compact space S1] is studied in the hamiltonian framework. Without using a gauge fixing condition, gauge degrees of freedom are eliminated by explicitly solving Gauss' law. The resulting effective hamiltonian describes interacting fermions coupled to a finite number of quantum mechanical variables representing the physical Yang-Mills degrees of freedom. The method can be trivially extended to other gauge theories with matter on a cylinder.