The current article is devoted to the nonlinear dynamic and impact response analyses of rectangular incompressible neo‐Hookean hyperelastic plates with uniform/nonuniform transverse distributions of stiff elastic reinforcing particles. The nonlinear finite element governing equations are derived by using the principle of minimum total potential energy and solved by an updating scheme that uses the Runge‐Kutta time integration and penalty methods. The impact energy expressions are written for the integrated plate‐indenter system. The novelties of the article are: (i) realistic modeling the energy absorption of a particle‐reinforced nonlinear hyperelastic matrix based on the volume fractions of the constituent phases instead of using wrong Voigt‐type models or impractical predefined gradation coefficients, (ii) considering non‐uniform distributions of the reinforcing particles, (iii) using a highly accurate asymmetric (all the available theories are symmetric) infinite‐order plate theory, (iv) including the inherent hyperelastic nature of the material in the definition of the parameters of the plate theory, (v) considering the thickness changes of the plate, (vi) including von Karman's kinematic nonlinearity, (vii) analyzing both the dynamic and impact behaviors, (viii) proposing an adaptive algorithm to match the description of the displacement field with the load/stress variations, (ix) updating not only the stiffness but also the mass matrix within the time steps, (x) incorporation of the nonlinear boundary conditions by the penalty method, and (xi) performing time‐dependent analyses instead of the natural frequency analyses. Results reveal the drastic effects of the volume fraction of the reinforcing particles on the dynamic responses and report the impact responses of the FG hyperelastic plates, for the first time.