In this present note, we formulate a model for hybrid dynamical systems with delay, which covers a large class of delay systems. Under several mild assumptions, we establish sufficient conditions for uniform asymptotic stability of hybrid dynamical systems with delay via Lyapunov-Razumikhin technique. To demonstrate the developed theory, we conduct stability analyzes for delay sampled-data feedback control systems including a nonlinear continuous-time plant and a linear discrete-time controller.