Numerical inversion of almost arbitrary Laplace transforms, for any value of t, to any prescribed accuracy up to atleast three-quarters of the computer precision, is effected by trapezoidal integration along a special contour. The required number of points depends on t, the accuracy, and the transform singularity positions, and for moderate t is typically 11 for errors of order 10−6, 18 for order 10−10, 35 for order 10−20(with double precision working).