We consider the following two plane mixed problems of the theory of elasticity. The problem of stretching a strip weakened by two equal length longitudinal silts, and the problem of longitudinal splitting of a strip by means of a wedge of finite length ( ∗). In the second problem, slits appear on each side of the wedge. Both, the slits and the wedge are symmetrical with respect to the edges of the strip. The method of solution employed is analogous to that developed in [2]. The formulas obtained define the form of the slit surface and the normal stress intensity coefficient, and represent asymptotic expansions of the exact solutions in negative powers of the parameter γ = h/ b characterizing the relative thickness of the strip.