Biological tissues have become a major focus in computational mechanics because of their crucial role in practical applications. One such application is the simulation of neurosurgical procedures, which requires reliable numerical tools to model the deformation and cutting of brain tissue. Peridynamics, a non-local continuum theory of mechanics, is particularly suitable for this task, as it can effectively capture the evolution of discontinuities like those created during surgical incisions. Among the peridynamic approaches, the correspondence models [1] stand out for their flexibility in modeling complex constitutive laws, such as the viscohyperelastic formulations commonly used to describe the mechanical behavior of cerebral tissue. However, these models require stabilization methods to eliminate zero-energy modes that can compromise numerical accuracy [2]. In our study, we identified a key challenge in this context, namely the issue of volumetric locking, which leads to an artificially stiff response when simulating nearly-incompressible soft materials. To address this, we introduce a straightforward strategy to alleviate volumetric locking in stabilized peridynamic correspondence models. The proposed method is validated through various numerical experiments involving hyperelastic materials, demonstrating improved performance and accuracy. REFERENCES [1] S.A. Silling, M. Epton, O. Weckner, J. Xu, E. Askari. Peridynamic states and constitutive modeling. Journal of Elasticity (2007) 88(2): 151-184. [2] H. Chen. Bond-associated deformation gradients for peridynamic correspondence model. Mechanics Research Communications (2018) 90: 34-41.