  It is shown that the cuspy density distributions observed in the cores of
elliptical galaxies can be realized by dissipationless gravitational collapse.
The initial models consist of power-law density spheres such as $\rho\propto
r^{-1}$ with anisotropic velocity dispersions. Collapse simulations are carried
out by integrating the collisionless Boltzmann equation directly, on the
assumption of spherical symmetry. From the results obtained, the extent of
constant density cores, formed through violent relaxation, decreases as the
velocity anisotropy increases radially, and practically disappears for
extremely radially anisotropic models. As a result, the relaxed density
distributions become more cuspy with increasing radial velocity anisotropy. It
is thus concluded that the velocity anisotropy could be a key ingredient for
the formation of density cusps in a dissipationless collapse picture. The
velocity dispersions increase with radius in the cores according to the nearly
power-law density distributions. The power-law index, $n$, of the density
profiles, defined as $\rho\propto r^{-n}$, changes from $n\approx 2.1$ at
intermediate radii, to a shallower power than $n\approx 2.1$ toward the centre.
This density bend can be explained from our postulated local phase-space
constraint that the phase-space density accessible to the relaxed state is
determined at each radius by the maximum phase-space density of the initial
state.
