Basic principles controlling tensional failure of a solid are applied in this work to investigate the role played by angularities. The conditions explored apply equally to the initial rupture of sections of the walls of a magma chamber or reservoir and to the propagation of the leading edge of a three dimensional intrusion. The results show that even when the internal pressure inside a cavity might be uniform, the resulting stress on the material surrounding it can have contrastingly different values depending on its position relative to any angularities. Such variability explains why similar volumes of magma, trapped under similar conditions at depth and therefore having equivalent buoyancy, sometimes may feed a tapping event and fail to do so at other times. In addition, it can be appreciated why sometimes veins and dykelets only a few millimeters thick are formed whereas on other occasions it is possible to create a dyke several meters wide filled with magma of similar composition and intruding very similar country rock. The approach followed here also provides an alternative mechanism for the formation of blunt-ended dykes, and outlines the form in which those intrusions are likely to evolve under certain circumstances.