Transform and non-transform discontinuities that offset slow spreading mid-ocean ridges involve complex thermal and mechanical interactions. The truncation of the ridge axis influences the dynamics of spreading and accretion over a certain distance from the segment-end. Likewise, the spreading system is expected to influence the lithospheric plate adjacent to the ridge-end opposite of the discontinuity. Tectonic effects of the truncated ridge are noticeable in for example the contrast between seafloor topography at inside corners and outside corners, along-axis variations in rift valley depth, style of crustal accretion, and ridge segment retreat and lengthening. Along such slow-spreading discontinuities and their fossil traces, oceanic core complexes or mega-mullion structures are rather common extensional tectonic features. In an attempt to understand deformation of oceanic lithosphere near ridge offsets, the evolution of discontinuities, and conditions that may favor oceanic core complex formation, a three-dimensional thermo-mechanical model has been developed. The numerical approach allows for a more complete assessment of lithosphere deformation and associated stress fields in inside corners than was possible in previous 3-D models. The initial suite of results reported here focuses on deformation when axial properties do not vary along-strike or with time, showing the extent to which plate boundary geometry alone can influence deformation. We find that non-transform discontinuities are represented by a wide, oblique deformation zone that tends to change orientation with time to become more parallel to the ridge segments. This contrasts with predicted deformation near transform discontinuities, where initial orientation is maintained in time. The boundary between the plates is found to be vertical in the center of the offset and curved at depth in the inside corners near the ridge-transform intersection. Ridge-normal tensile stresses concentrate in line with the ridge tip, extending onto the older plate across the discontinuity, and high stress amplitudes are absent in the inside corners during the magmatic accretionary phase simulated by our models. With the tested rheology and boundary conditions, inside corner formation of oceanic core complexes is predicted to be unlikely during magmatic spreading phases. Additional modeling studies are needed for a full understanding of extensional stress release in relatively young oceanic lithosphere.