The impact behavior of composite materials has been extensively studied but interest has been centered on flat plates. For underwater applications, thick composite cylinders are employed and several questions must be addressed concerning the influence of accidental impact. The aim of this work is to study the dynamic response of tubular structures. Such structures find many applications but the damage upon impact is not taken into account during their dimensioning. However, at the time of their handling or in service the damage introduced by accidental impact can compromise their capacity to fulfill their function. The cylinders are thick and consist of epoxy matrix and glass fiber reinforcement. After having observed the nature of the damage related to the static and dynamic loading, the scale and size effects on dynamic response and damage are examined. The studies reveal that the dynamic responses show a satisfactory correlation with predictions based on rules of similitude.