<p>Peridynamics is a theoretical framework that utilizes integro-differential equations as an alternative to the traditional partial differential equations employed in classical continuum mechanics. The theory of peridynamics incorporates the horizon’s size as a nonlocal length parameter, hence classifying it as a nonlocal theory. In this study, an approach is presented for the implementation of nonlocal Helmholtz decomposition, which decomposes the displacement field into components that are divergence-free and curl-free. This work introduces the peridynamic field decomposition within the framework of nonlocal vector calculus. As a consequence, two integral governing equations were derived, which were associated with potential fields. The dispersion relation for longitudinal and transverse waves is determined by analyzing the harmonic solutions of the plane wave. The general solutions for initial-value problems are derived in closed-form expression by utilizing Green’s function. The variations in frequency, phase velocity, and group velocity with changes in nonlocal length parameters and nonlocality functions are demonstrated. The validation is achieved by restricting the scenario to the classical limit when the nonlocal length approaches zero. This work implements nonlocal Helmholtz decomposition, a robust framework that simplifies the study and provides comprehensive insight while analyzing vector fields.</p>