This paper aims at developing an aeroelastic model for the instability analysis of supersonic thick fins. To this aim the modal analysis technique is used for the structural dynamics modelling of a fin with a general structure. An unsteady aerodynamic model is applied based on the shock/expansion analysis over the flat surfaces of the fin along with local application of the piston theory. Assuming a supersonic fin with an arbitrary polygonal cross-section, thickness and initial angle-of-attack, the steady flow properties (e.g. Mach number, density and temperature) are calculated over the flat surfaces of the fin. Then, assuming small amplitude vibrations, the generalised aerodynamic forces are obtained in terms of the structural modal coordinates. Using the obtained model, the effect of thickness, initial angle-of-attack, taper ratio and sweep angle on the aerodynamic derivatives and aeroelastic stability of the fin are studied which show their remarkable effects on the instability Mach number and its type. Specially, the presented results show that increasing the fin thickness dramatically diminishes the stability margin mainly at low angles of attack. Also a sharp decrease of the divergence Mach number is observed by increasing the fin’s incidence angle.