The term Leak-Before-Break (LBB) refers to a well-established safety criterion used to assess whether cracked tanks or pipes can leak detectable amounts of fluid as a warning before catastrophic failure occurs. In this research The LBB criterion was applied to the safety assessment of spherical Liquefied Natural Gas (LNG) containment systems on ships. For this type of LNG tanks, the International Code for the Construction and Equipment of Ships Carrying Liquefied Gases in Bulk (IGC) requires several fracture mechanics analyses of fatigue crack growth. Details on how these analyses should be carried out can be found in industry codes. Although these codes provide guidance on most aspects of an LBB assessment, they are not fully satisfactory with regard to their recommendations on how to calculate the growth of deep semi-elliptical surface cracks, on how to estimate the crack shape when the crack snaps through the tank wall and how to assess these through-thickness cracks in the stage right after breakthrough. The aim of this research was to more accurately simulate the development of cracks for LBB applications. To do so, a new numerical calculation model have been developed for the estimation of crack growth, crack shape development and crack propagation after wall penetration. In addition, Finite Element Models (FEM) have been developed to predict the Stress Intensity Factor (SIF), a parameter that characterises the local stress distribution in the vicinity of a crack-tip and is commonly used in fracture mechanics. Finite Element (FE) analyses were conducted to evaluate existing, approximative SIF solutions for deep, semi-elliptical surface cracks and to find a new, FE-derived SIF solution for through-thickness cracks after breakthrough. Both the new FE-derived and existing SIF solutions were used in the numerical model. The results of different SIF solutions and numerical model configurations were then compared to experimental data from the literature in order to find recommendations for the enhancement of existing LBB procedures.