Abstract. In this investigation, the authors intend to study the dynamic instability (flutter) of variable stiffness composite laminates (VSCLs) in the presence of supersonic flow. In the type of VSCL considered here, plies have curvilinear fibres and, consequently, the stiffness is variable in a macroscopic view. The plates considered are rectangular. In each ply, a reference fibre path, represented by a function of horizontal coordinate x, is defined. The reference fibre path orientation changes linearly from T 0 at the centre to T 1 at both vertical edges of the ply; the other fibre paths are defined shifting the reference path in direction y. The displacement and rotations are defined using a Third-order Shear Deformation Theory, and then they are discretised by a p-version finite element model that applies to VSCL plates. Piston theory is employed to model the aerodynamic force of the upstream flow in direction x. Flutter airspeeds are investigated for VSCL plates with different fibre angles. Changes of flutter speed are evaluated in two different regimes of steady and unsteady flow.