In linear mechanics [I0, Ii, 15-19, 21, 22], brittle and quasibrittle fracture by the initial stress (compressive or tensile) acting along a surface in which there are cracks is not found to have any effect on the distribution of the stress--strain state around the end of the crack, and hence on the breakdown criterion. The effect of such an initial stress may be taken into account within the framework of linearized elasticity theory [2-4]. The present work is devoted to formulating linearized static problems of determining the stress-strain state around a crack for elastic bodies with an initial stress and constructing accurate solutions for bodies with an infinite plane normal-tear crack. The investigation utilizes the complex potentials introduced in [6, 7, 9] and the methods of solving mixed problems of classical elasticity theory developed in [i, 12, 14, 21], i.e., methods of solving the Riemann--Hilbert problem and the Keldysh--Sedov formula [12, 21]; the relations and notation of [2-7] are used, and all quantities referring to the initial state are denoted by a zero subscript; the investigation is conducted in the cartesian coordinates of the initial state, yj (j = i, 2, 3), and all quantities are referred to the dimensions of the body in the initial stress--strain state.