We study the physical processes controlling the development and evolution of normal faults by analyzing numerical experiments of extension of an ideal two-dimensional elastic-plastic (brittle) layer floating on an inviscid fluid. The yield stress of the layer is the sum of the layer cohesion and its frictional stress. Faults are initiated by a small plastic flaw in the layer. We get finite fault offset when we make fault cohesion decrease with strain. Even in this highly idealized system we vary six physical parameters: the initial cohesion of the layer, the thickness of the layer, the rate of cohesion reduction with plastic strain, the friction coefficient, the flaw size and the fault width. We obtain two main types of faulting behavior: (1) multiple major faults with small offset and (2) single major fault that can develop very large offset. We show that only two parameters control these different types of faulting patterns: (1) the brittle layer thickness for a given cohesion and (2) the rate of cohesion reduction with strain. For a large brittle layer thickness (>22 km with 44 MPa of cohesion), extension always leads to multiple faults distributed over the width of the layer. For a smaller brittle layer thickness the fault pattern is dependent on the rate of fault weakening: a very slow rate of weakening leads to a very large offset fault and a fast rate of weakening leads to an asymmetric graben and eventually to a very large offset fault. When the offset is very large, the model produces major features of the pattern of topography and faulting seen in some metamorphic core complexes. ¿ 2000 American Geophysical Union