An infinite elastic solid containing a doubly periodic rectangular array of slitlike cracks is considered. The solid is subjected to a uniform stress resulting in a state of plane strain. The cracks are represented as suitable distributions of dislocations which are determined from a singular integral equation. This equation is solved numerically in an efficient manner using an expansion of the nonsingular part of the kernel in a series of Chebyshev polynomials. Values of the stress-intensity factors are presented, as well as the change in strain energy due to the presence of the cracks. Also, the effective elastic constants of a sheet having a rectangular array of cracks are given as functions of the crack spacing.