  We study the geometry of a wormhole spacetime filled with anisotropic matter
in the context of general relativity. In the course of the study, new static
and spherically symmetric solutions, analytic and numerical ones, are found. We
specify the existence condition for a wormhole throat. We analyze properties of
the solutions after categorizing them based on the spacetime regularity and the
signature of energy density. The necessary conditions which allow a wormhole
spacetime to be nonsingular are described.
