Calving is the process of blocks of ice detaching from an ice shelf of grounded calving cliff. Here, we focus on calving that occurs through the propagation of fractures through a floating ice shelf on sufficiently short time scales to allow ice rheology to be treated as elastic. We revisit the linear elastic fracture mechanics models of Weertman and van der Veen, which consider the propagation of cracks into slabs of ice, driven by an applied extensional stress and by water pressure inside the crack, due to sea water and surface melt entering the cracks. We extend their work by considering the interaction between multiple cracks and developing a method that allows us to compute crack propagation in arbitrary domain geometries. We show that the simple case of two aligned cracks, one extending from the ice surface and the other from the base, can be considered as a two-dimensional dynamical system. We are able to show that viable steady crack configurations (where the ice shelf is crevassed without calving) correspond to stable fixed points of that dynamical systems. Calving corresponds to the annihilation of steady states under a parameter change. That can either take the form a bifurcation that happens at specific combinations of forcing parameters, and leads to the abrupt, dynamic propagation of the crack across the remaining unbroken thickness of ice. Alternatively, calving can occur because the two crack tips gradually meet as forcing parameters change. We derive different forms of calving laws, depending on whether crack propagation to full calving is initiated from a previously un-cracked floating slab of ice, or from a previously cracked configuration. For the former, we show that calving laws take the form of a functional relationship between a water storage parameter, extensional stress, ice thickness and fracture toughness. For the latter, we obtain an history-dependent relationship in the form of a steady crack evolution problem that bears abstract similarity with plasticity models. We also discuss how these could be implemented in ice flow models.