In the framework of the theory of subcritical crack development in viscoelastic bodies (see \textit{A.~A.~Kaminskii} and \textit{G.~V.~Gavrilov}, Prikl. Mekh. 34, No.~11, 60--66 (1998)) the initial stage of the subcritical crack development in the aging composite plate under constant external loading is investigated in terms of the generalized method of operator chain fractions which was proposed and substantiated in [\textit{A.~A.~Kaminskii}, ``Failure of viscoelastic bodies with cracks'', Naukova Dumka , Kiev (1990)].