In an effort to arrive at a dynamical model for the interstellar medium, its mechanical properties are discussed. Using a polytrope relation between the temperature and density within a gas cloud, the mechanical and then the statistical properties of an idealized model of the interstellar clouds are developed. One finds that the collision rate of clouds, computed in an elementary fashion from their diameters and random translational velocities, leads to several difficulties. First, the very inelastic nature of head-on collisions would rapidly reduce the translational velocities, and it would be difficult to explain the observed radial velocities. Second, there would be a strong tendency toward statistical equilibrium of the internal state of the clouds. The equilibrium is investigated, and the cloud is found to be either in a collapsed condition or completely dispersed, again contrary to observation. Ordering of the translational velocities is proposed as one means of circumventing these difficulties. In any case, the tendency of clouds to collapse, possibly to form clusters of stars, is shown to be intrinsic in their nature.