In this paper we investigate the dynamics of robotic interception and capture of a moving object. This problem, i.e., the interception and capture of a moving object by a robot, is called dynamic mass capture. The effects of structural flexibility of the robot is taken into consideration. In terms of time, the analysis is divided into three phases: before capture (finite motion), at the vicinity of interception and capture (impulsive motion), and after capture (finite motion). Special attention is paid to the modeling of the second phase when the robot captures the target and it becomes part of the end effector, thus, the system''s degrees of freedom suddenly change. To decribe this event, a novel approach is proposed. This is based on the use of a class of impulsive constraints, the so-called inert constraints. Jourdain''s principle is employed to derive the dynamic equations for both finite and impulsive motions. Simulation results are presented for two examples: a single flexible link and a two-link manipulator capturing moving objects. In the example of the single link, the results are compared with the observations of an experiment, and good agreement is found between experimental and simulation results.