Recently, Hershel observation has revealed that filaments are fundamental structure forming interstellar molecular clouds. In addition, magnetic field, which is believed to be important in supporting the cloud, is observed perpendicular to the filament. We studied the magnetohydrostatic equilibrium structure of the filament with prependicular magnetic field. Two types of magnetohydrostatic structure are found. Critical mass (maximum supported mass against gravity) is obtained as a function of the magnetic flux. It is shown that the critical line-mass lambda is proportional to the magnetic flux per unit length Phi as lambda ~ 0.24 Phi / G^1/2. Polarization pattern expected for the magnetized filaments is also studied. The interstellar polarization shows both perpendicular and parallel pattern to the filament depending on the line-of-sight. We discuss the configuration of the magnetic field expected from the interstellar polarization.