  Many astrophysical sources of high energy emission, such as black hole
magnetospheres, superstrongly magnetized neutron stars (magnetars), and
probably relativistic jets in Active Galactic Nuclei and Gamma Ray Bursts
involve relativistically magnetically dominated plasma. In such plasma the
energy density of magnetic field greatly exceeds the thermal and the rest mass
energy density of particles. Therefore the magnetic field is the main reservoir
of energy and its dissipation may power the bursting emission from these
sources, in close analogy to Solar flares. One of the principal dissipative
instabilities that may lead to release of magnetic energy is the tearing
instability. In this paper we study, both analytically and numerically, the
development of tearing instability in relativistically magnetically-dominated
plasma using the framework of resistive magnetodynamics. We confirm and
elucidate the previously obtained result on the growth rate of the tearing
mode: the shortest growth time is the same as in the case of classical
non-relativistic MHD, namely $\tau =\sqrt{\tau_a \tau_d}$ where $\tau_a$ is the
\Alfven crossing time and $\tau_d$ is the resistive time of a current layer.
