Composite materials are artificially made materials used in various mechanical applicationsrnlike shells and plates. Composite materials are nowadays commonly used in the aviationrnindustry and marine application in the form of vessels or shells. In this work the stress andrnstrain distributions around the surface cracked cylindrical shell structure have beenrnpresented by studying, the effect of the crack length and direction on stress, anisotropicrnelasticity relations and stress field equations of surface crack problems in compositernmaterials, finally finite element method simulation is applied to investigate the stress andrnstrain distribution around the surface crack in a composite material cylindrical shellrnstructure.rnMathematical modeling and finite element simulation of the surface cracked cylindricalrnshell was performed and the problem was finally solved using ANSYS finite elementrnmethod package.rnIn general, the maximum Von Misses stress at the crack tip generally increase as crackrnlength increase and the internal axial crack orientation has shown the maximum critical vonrnMisses stress distribution around the surface crack because of the nature of curvedrngeometry of the shell structure and the far field tangentially applied stress tries to open thernsurface crack.