Time-dependent, three-dimensional (3-D) particle simulations of an accretion disk interacting with an incoming stream were performed as a model for disks in close binary systems. We first confirmed the results of two-dimensional simulations; when the mass ratio, q = M2/M1 (M1 and M2 are the masses of a compact object and a companion star, respectively), is unity, the disk is stable for the tidal instability and thus settles into a steady-state structure. If, on the other hand, q is small, say 0.15, the tidal instability is initiated when the radius of the disk exceeds a certain critical value, leading to the formation of a precessing, eccentric accretion disk. We next examined the three-dimensional effects. The half-thickness of the disk, which is calculated assuming a Gaussian density profile in the vertical direction, is much larger everywhere in the outer portions of the disk than the value expected from hydrostatic balance; the ratio of the vertical height (H) to the radius (r) is on average 10-20%, and is especially enhanced at the eclipse phases, approximately 0.8 and 0.2 (there is also a small peak at 0.5), where H/r approximately 0.15. This is a result of a violent collision of the incoming stream with disk material. The gas in the disk is hit by the stream, thereby being given a vertical velocity component, which results in material moving up and down in the vertical direction with the Keplerian time-scale of the outer rim. Finally, we suggest that the calculated extended rim structures are quite reminiscent of what is indicated from the orbital X-ray variation in some X-ray binaries, such as the accretion disk corona sources and the dipping sources, and in some dwarf novae, such as U Gem and OY Car.