  We compute chromoelectric and chromomagnetic flux densities for hybrid static
potentials in SU(2) and SU(3) lattice gauge theory. In addition to the ordinary
static potential with quantum numbers $\Lambda_\eta^\epsilon = \Sigma_g^+$, we
present numerical results for seven hybrid static potentials corresponding to
$\Lambda_\eta^{(\epsilon)} = \Sigma_u^+, \Sigma_g^-, \Sigma_u^-, \Pi_g, \Pi_u,
\Delta_g, \Delta_u$, where the flux densities of five of them are studied for
the first time in this work. We observe hybrid static potential flux tubes,
which are significantly different from that of the ordinary static potential.
They are reminiscent of vibrating strings, with localized peaks in the flux
densities that can be interpreted as valence gluons.
