Composite materials are combinations of two or more materials giving a third materialrnwith highly desirable properties. A composite material cylindrical shell is one of therncomponents used in weight sensitive areas as composite materials are nowadaysrncommonly used in the aviation industry and marine applications. In many practicalrnapplications, using composites is more efficient. For example, in highly competitive airlinernmarkets, one is continuously looking for ways to lower overall mass of the aircraft withoutrndecreasing the stiffness and strength of its components like cylindrical shells or pressurernvessels. This is possible by replacing conventional metal alloys with composite materials.rnHowever, surface irregularities and micro cracks can be imparted to such materials forrnvarious reasons and it is very important to analyze these materials carefully to hinder therndamage that could result as a result of failurernIn this work the stress and strain distributions around the surface cracked cylindrical shellrnstructure have been presented by studying the properties of composites, anisotropicrnelasticity relations, stress intensity factors, fracture toughness and stress field equations ofrnsurface crack problems in composite material, and finally finite element methodrnsimulation is applied to investigate the stress and strain distribution around the surfacerncrack in a composite material cylindrical shell structure.rnMathematical modeling and finite element simulation of the surface cracked cylindricalrnshell was performed and the problem was finally solved using ANSYS finite elementrnmethod package. In the mean time, results were obtained in the post processing stage ofrnANSYS. The main results obtained were the variation of the critical stress and strainrndistributions around the surface crack which could be cold shielded damaged zone thatrnmakes composite materials having unpredicted damage zone sizes. Finally, the criticalrnstress and strain distribution patterns, the crack propagation schemes or styles wererncompared with literatures from composite material shell structures and conventionalrnisotopic materials to draw conclusions regarding the advantages of composites comparedrnto conventional material in crack advancementrnKey words: Composite materials, anisotropic stress-strain relationship, laminate,rnsurface crack, shielding effect, crack simulation, classical shell theory.