<p>This paper considers the forced vibrations of nonlinear wave equation in a ball with arbitrary spatial dimension and radius. We mainly focus on the influence of periodic external force and study the existence of response solutions which are excited by the external force and share the same frequency as the external force. By developing the Lyapunov–Schmidt reduction method and designing a differential Nash–Moser iterative scheme, we obtain the existence of radially symmetric response solutions for the forced wave equation with finitely differentiable nonlinearity. It is worth mentioning that our approach allows for arbitrary spatial dimension and radius as well as a large measure set of frequencies.</p>