  We analyze $\mu^+\mu^-$ pair production generated by high-energy electrons
emerging from a laser-wakefield accelerator. The $\mu^+\mu^-$ pairs are created
in a solid thick high-$Z$ target, following the electron accelerating plasma
region. Numerical estimates are presented for electron beams obtained presently
in the LBL TW laser experiment \cite{C2} and possible future developments.
Reactions induced by the secondary bremsstrahlung photons dominate the dimuon
production. According to our estimates, a 20 pC electron bunch with energy of 1
(10) GeV may create about 200 (6000) muon pairs. The produced $\mu^\pm$ can be
used in studying various aspects of muon-related physics in table top
installations. This may be considered as an important step towards the
investigation of more complicated elementary processes induced by laser driven
electrons.
