  We investigate effects of the magnetic field on the propagation of laminar
flames of nuclear reactions taking place in white dwarfs (WDs) with the mass
close to the Chandrasekhar limit. We calculate the velocities of laminar flames
parallel and perpendicular to uniform magnetic fields as eigenvalues of steady
solutions for magnetic hydrodynamical equations. As a result, we find that even
when the magnetic pressure does not dominate the entire pressure it is possible
for the magnetic field to suppress the flame propagation through the thermal
conduction. Above the critical magnetic field, the flame velocity decreases
with increasing magnetic field strength as $v \sim B^{-1}$. In media with
densities of $10^{7}, 10^{8}, \,\mathrm{and}\,10^{9} \unit{g\,cm^{-3}}$, the
critical magnetic fields are orders of $\sim 10^{10}, 10^{11},
\,\mathrm{and}\,10^{12} \unit{G}$, respectively.
