Monte Carlo simulations of tethered chain conformations in spherical cavities were performed in a relatively broad range of average segment densities (both the number of chains and their lengths were varied). A special attention was paid to dense systems which may be considered suitable models for studying the behavior of insoluble blocks in cores of block copolymer micelles in selective solvents. Simulations were performed on a tetrahedral Lattice using (i) the mutually independent simultaneous self-avoiding growths of all chains and (ii) a modified equilibration algorithm similar to that developed by Siepmann and Frenkel, Only the geometric exclusion effect of segments was considered since it plays the dominant role in dense systems without strong, or specific, interactions. Various distribution functions (e.g., distribution of the end-to-end and the end-to-gravity center distances and their orientations with respect to the radial direction, or to the direction of the first-to-second segment connection, etc.) were calculated, and the effect of increasing average segment density, the number of chains, and their increasing length, etc. was studied. It was found that the conformational characteristics of short tethered chains in constrained volumes (mainly those that describe orientations of chains with respect to the radial direction) are affected by the average segment density only a little, whereas properties of long tethered chains depend very sensitively on the density. They change mainly in the region of low and medium densities. Distribution functions of both short and long chains are fairly similar at high densities. Dense systems of tethered chains in small closed volumes are generally highly disordered.