The coupling of advanced structural and aerodynamic methods is a complex and computationally demanding task. In many cases, simplifications must be made. For the flight simulation of flexible aerospace vehicles, it is common to reduce the overall structure down to a series of linked degenerate structures such as Euler-Bernoulli beams in order to expedite the structural portion of the solution process. The current study employs the sophistication and generality of finite-element based modeling with the concepts of reduced-order modeling to create a general flexible-body flight simulation program. The program was created for use with the MATLAB-Simulink programming package. A parametric analysis on the stability of flexible rockets is performed and results are presented for a variety of rocket configurations based on the SPHADS-1 vehicle under development at Ryerson University. The primary instability mode under study is that associated with the flapping and twisting motions of the tailfins under aerodynamic loading. By varying the average fin thickness, both stable and unstable behaviour is recorded for a variety of flight conditions.