In order to analyse the deformation response of materials and structures, various continuum mechanics theories have been proposed. Peridynamics is a new non-local continuum mechanics formulation which has governing equations in integro-differential equation form. Analytical solution of these integro-differential equations is limited in the literature. In this study, analytical solution of the peridynamic equation of motion for a 2-dimensional membrane is presented. Analytical solutions are obtained for both static and dynamic conditions. Various numerical cases are considered to validate the derived analytical solution by comparing peridynamic results against classical continuum mechanics results. For both static and dynamic cases, both solutions agree very well with each other. Moreover, the influence of the size of the length scale parameter in peridynamics, horizon, is investigated. According to the numerical results, it is concluded that as the horizon size becomes larger, peridynamic solution captures nonlocal characteristics and peridynamic results deviate from classical continuum mechanics results.