The Virtual Element Method (VEM) has been widely applied in solid mechanics, spanning from linear elasticity to fracture analysis. A key feature of VEM is its ability to reconstruct internal fields using only the displacement interpolation along the element boundary. This characteristic enables the development of polygonal elements with reduced sensitivity to mesh distortion compared to classical Finite Elements (FEs). However, this flexibility comes at the cost of stabilization procedures, which remain a major challenge, particularly in nonlinear applications. In this work, we propose a stabilization-free Virtual Element formulation for limit and shakedown analyses of 2D problems. The approach is developed within the Hybrid VEM (HVEM) framework, leveraging an energy norm in the VE projection and a high-order self-equilibrated stress interpolation. This formulation can be interpreted as an extension of the hybrid FEM to polygonal geometries. The stress basis dimension is carefully selected to ensure rank sufficiency, thereby eliminating the need for stabilization terms. For structures subjected to multiple load cases, the shakedown load multiplier is determined by constructing a pseudo-equilibrium path comprising a sequence of safe states with a monotonically increasing load factor. Each state is obtained by identifying kinematic variables that correspond to self-equilibrated stresses satisfying Melan’s condition. Benchmark tests on classical 2D problems demonstrate the accuracy of HVEM for coarse meshes and its high convergence rate in computing collapse and shakedown loads. In particular, HVEM proves to be particularly suitable for shakedown analyses, given its accuracy in both elastic and elastoplastic regimes. Moreover, as shown in plane-strain problems, the proposed HVEM formulation is free from volumetric locking.