  We consider magnetohydrodynamical interaction between relativistic pulsar
wind and static magnetosphere in binary pulsar system PSR J0737-3039. We
construct semi-analytical model describing the form of the interface separating
the two pulsars.
  An assumption of vacuum dipole spin down for Pulsar B leads to eclipse
duration ten times longer than observed. We discuss possible Pulsar B torque
modification and magnetic field estimates due to the interaction with
  Pulsar A wind.
  Unless the orbital inclination is $\leq 86 ^\circ$, the duration of eclipses
is typically shorter than the one implied by the size of the eclipsing region.
We propose that eclipses occur due to synchrotron absorption by mildly
relativistic particles in the shocked Pulsar A wind. The corresponding optical
depth may be high enough if Pulsar A wind density is at the upper allowed
limits. We derive jump conditions at oblique, relativistic,
magnetohydrodynamical shocks and discuss the structure of the shocked Pulsar A
wind. Finally, we speculate on a possible mechanism of orbital modulation of
Pulsar B radio emission.
