  One of the most promising sources of gravitational radiation is coalescence
of binary neutron stars or black holes. In order to study gravitational
radiation at the merging phase of coalescing binary neutron stars which is
called the last three-milliseconds, full general relativistic simulations are
required. Since coalescence of binary stars is a completely non-axisymmetric
and 3 dimensional (in space) event, which needs great powers of computers, we
have to develop a method of 3D numerical relativity using a vector-parallel
supercomputer. As a first step of this final goal, we started simulations using
post-Newtonian hydrodynamics including radiation reaction of gravitational
waves from 1989. They gave a lot of perspectives on coalescing events and
gravitational radiation from them. Next we started to attack 3D, fully
relativistic simulations. First, basic equations on the (3+1)-formalism of the
Einstein equations are shown. As for gauge conditions, we use conformal time
slicing and psuedo minimal distortion condtions at present. For these
conditions as well as to solve initial value equations, we should solve some
elliptic partial differential equations. It consumes the greatest part of CPU
time. We show recent results of test simulations on coalescing binary neutron
stars.
