An electrostatic linear analysis is performed for a finite‐width electron or ion beam streaming along a strong magnetic field in the presence of a homogeneous background plasma. The linear fluid equations have been solved as a boundary value problem for planar and cylindrical beam shapes, and the dispersion which results as an eigenvalue problem is solved numerically without approximation as a function of the electron beam width. The solution gives unstable modes for any beam width and the dispersion relation shows different branches. There is a branch in both configurations that represents the most unstable mode, and the wavelength of this unstable mode for the cylindrical beam is larger than the corresponding wavelength for the most unstable mode of the slab‐shaped beam.