An eigenfunction expansion technique, based in part on separation of the thickness-variable and partly on the Eshelby-Stroh type affine transformation, is employed to derive hitherto unavailable threedimensional asymptotic stress field in the vicinity of the front of a semi-infinite through-thickness crack weakening an infinite transversely isotropic unidirectional fiber reinforced composite plate, of finite thickness and subjected to far-field mode I/II loadings. Crack-face boundary conditions and those that are prescribed on the top and bottom (free, fixed or lubricated) surfaces of the lamina are exactly satisfied. The present investigation considers mainly two through-crack systems -(i) (0 1 0)[0 0 1] with the [1 0 0] propagation direction, and (ii) Γ° 1 0 0ΓΒ½0 0 1 with the [0 1 0] propagation direction. Explicit expressions for the singular stresses in the vicinity of the front of a through-thickness crack weakening a transversely isotropic unidirectional fiber reinforced composite plate, subjected to far-field mode I/II loadings, are presented. Hitherto unavailable numerical results, pertaining to the through-thickness variations of stress intensity factors for saw-tooth load and its skew-symmetric counterpart that also satisfy the boundary conditions on the top and bottom surfaces of the cracked unidirectional fiber reinforced composite (transversely isotropic) plates under investigation, bridge a longstanding gap in the fracture mechanics literature.