Problems of dynamic response of composites subject to impact are important both for theory and in practical applications. In this paper three such problems are considered: slamming of composite plates; sloshing of cylindrical tanks manufactured from composite materials; and dynamic buckling of thin composite plates with initial imperfections. The closed form solution of the first two problems is obtained by the convolution integral. The third problem is reduced to a single nonlinear differential equation which is integrated numerically. These solutions can be easily extended to other composite structures (cylindrical panels in the first and the third problems; spherical tanks in the second problem, etc. ) by using appropriate governing equations and the technique illustrated in the paper.