This document analyzes the motion of a tower of cylinders rolling without slipping on boards below and above each cylinder. It: 1) Models each pair of cylinders as a single cylinder with double the mass. 2) Derives equations relating the linear and angular accelerations of adjacent cylinders. 3) Diagnoses the stability of the system by analyzing the eigenvalues of the equation matrix, finding one eigenvalue corresponds to an exponentially growing solution and the other a decaying solution. 4) Concludes the initial conditions must correspond only to the decaying eigenvector solution for the system to be stable.