Distributions of total intensity and linear polarization have been calculated for synchrotron radiation from a variety of magnetic fields which may occur in extragalactic radio sources, assuming that the energy distributions of radiating electrons are uniform and isotropic. Analytical solutions are derived for helical and transverse self-similar fields of the type suggested for radio jets by Chan and Henriksen and compared with results for a field which has no component along the jet axis, but is otherwise random (as is expected to develop in an expanding jet containing a tangled field). A comparison with observation favors the last model, but is not conclusive; a search for variations of Faraday rotation across radio jets is suggested. The tangled-field model predicts that the fractional polarizations of jets are determined by their inclinations to the line of sight; it may therefore be possible to derive their three-dimensional structures. The polarization distributions of hot spots and extended radio lobes can be produced by magnetic fields which have been sheared also as to be tangential to the boundaries of the structures but which are otherwise random.