The interaction of through, surface, and internal cracks in shells of arbitrary curvature is examined. Crack of the same and different types with various geometry are considered. The curvature of the shell, the length and depth of the cracks, their arrangement and distance between them have a strong effect on the stress intensity factors for part-through cracks and on the force and moment intensity factors for through cracks Keywords: shell of arbitrary curvature; through, surface, and internal cracks; SIF; systems of singular integral equationsIntroduction. Shell structures often have surface or internal defects (cracks, inclusions, notches, etc.) of various geometry. In design models, defects are usually modeled by fictitious cuts. Note that the problem of stress distribution around a part-through crack of even perfect shape is three-dimensional, solving which involves severe mathematical difficulties. Such problems are usually solved with approximate methods. In particular, the line-spring model makes it possible to reduce the dimension of such problems by one, and it remains possible to model the depth profile of part-through cracks.The line-spring model helped to analyze the stress state of many isotropic plates and shells with surface and internal cracks [1,[12][13][14]. Cylindrical and spherical shells with longitudinal and transverse surface cracks are addressed in [7][8][9]. The stress state of a shell of arbitrary curvature with surface cracks of different length was first determined in [2,3]. Shells of arbitrary curvature with an internal crack and with a set of through and surface cracks oriented along both lines of principal curvatures are studied in [4-6].We will consider shells of arbitrary curvature weakened by cracks of different type and geometry oriented along both lines of principal curvatures.1. Problem Formulation Based on the Line-Spring Model. Consider a thin elastic isotropic shell of arbitrary Gaussian curvature and constant thickness h. We choose a system of orthogonal coordinates Oxyz so that the x-and y-axes are directed along the lines of principal curvatures of the shell's mid-surface, while the z-axis is directed along the normal to it. The shell is weakened by n through and part-through (surface or internal) cracks oriented along both lines of principal curvatures and is subjected to a symmetric external load.It is assumed that the crack faces are free from load and do not contact with each other during deformation.To solve the problem, we will use the line-spring model developed by Rice and Levy [14] to study an elastic plate with a surface crack. The main hypotheses that underlie the model were later generalized by Erdogan to a plate with internal crack [1,12].The tensile force and bending moment acting on the shell induce stresses in the interlayer at the front of the nth part-through crack. These stresses are described by unknown forces T p ( ) and moment M p ( ) in the line-spring model. After the introduction of T p ( ) and M p ( ) , we can regard the crack as a through one...