Jupiter’s satellite Europa is covered by an ice shell exhibiting many surface features, including linear structures called lineae, which in this work are treated as fractures. A three-dimensional finite-element simulator is used to numerically model fracture nucleation, growth, and interaction, assuming the ice is an isotropic, linear elastic medium. Tidal stresses are exerted upon the ice through the Jovian orbital relationship. These stresses are calculated using a closed-form model derived from first principles. The fractures grow in response to stress concentration around their tips, and a damage criterion models the weakening of the ice matrix. Three-dimensional non-planar multiple fracture growth is modelled as a function of geometric multi-modal stress intensity factors computed at the fracture tips. Fracturing is evaluated over multi-scale periods, from days to millions of years, thus capturing multiple tidal effects. Fracture behaviour is modelled across the Europan surface in one domain. The patterns are dense clusters of lineae about the stress maxima with diffuse fracturing in outlying regions. Fractures are also modelled in the vicinity of subsurface meltwater lenses, where fractures form parallel to the surface in contrast to the usual perpendicular orientation. The resultant fracture patterns are qualitatively compared against images from NASA’s Galileo mission. This work contributes to the understanding of Europan lineae by illustrating how they behave in a fracture mechanics framework, and suggests interesting results regarding lineae interaction with meltwater lenses. This work is also a proof of concept for this modelling approach, and will serve as the framework for future work.