  The calculation of the stress field around an arbitrarily shaped crack in an
infinite two-dimensional elastic medium is a mathematically daunting problem.
With the exception of few exactly soluble crack shapes the available results
are based on either perturbative approaches or on combinations of analytic and
numerical techniques. We present here a general solution of this problem for
any arbitrary crack. Along the way we develop a method to compute the conformal
map from the exterior of a circle to the exterior of a line of arbitrary shape,
offering it as a superior alternative to the classical Schwartz-Cristoffel
transformation. Our calculation results in an accurate estimate of the full
stress field and in particular of the stress intensity factors K_I and K_{II}
and the T-stress which are essential in the theory of fracture.

Materials Science