We present a detailed microphotoluminescence study of the long-range strain fields surrounding threading dislocations as well as their interaction and pattern formation in GaN bulk crystals. The stress patterns are detected by tiny energy shifts of the near-band-edge spectral lines and show a dipolelike stress state around the dislocation core of edge- or mixed-type dislocations, with an angular orientation coinciding with high-symmetry crystal directions. We detect tens of micrometers long linear lineups of edge dislocations with sizable effects on the local strain states and photoluminescence peak positions. With continuum elastic strain simulations, we demonstrate that the observed patterns of threading dislocations are energetically favorable. We calculated a binding energy per threading dislocation length of 50 meV/mu m against gliding of an edge dislocation within a lineup of edge dislocations of parallel Burgers vector orientation.