<p>In this paper, two types of viscoelastic composites (VECs) are proposed for constrained layer damping (CLD) treatment of axially loaded beams. The first type is a 2–2 VEC, which is comprised of the inclusion of aluminium foils within a rubber matrix. The same rubber matrix is used for the second type, which is a 1–3 VEC with the carbon-fiber layer reinforcement. The aim of these VECs is to improve the CLD treatment compared to traditional viscoelastic materials (VEMs), where this damping treatment is arranged through sandwich beam configuration. First, the effective complex stiffness properties of these VECs are determined. Next, a finite element (FE) model of the sandwich beam is developed to evaluate modal responses and static buckling loads. A reduced-order FE model is then developed in conjunction with the harmonic balance method to evaluate parametric instability regions. The numerical results reveal significantly reduced static buckling load when a VEM layer is incorporated within an axially loaded beam in sandwich configuration for CLD-based control of dynamic instability. It is found that this shortcoming of reduced static stability can be mitigated completely using the 2–2 or 1–3 VEC instead of the VEM. Moreover, the damping in the sandwich beam increases, enhancing its dynamic stability. Further results demonstrate the effects of the type of reinforcement and core-thickness on the stability characteristics. Overall, both the 2–2 and 1–3 VECs provide a significantly more effective CLD treatment than traditional VEMs to control the dynamic instability without compromising the static stability of axially loaded beams.</p>