Using two-dimensional numerical simulations, we have constructed a model for formation of a filamentary molecular cloud permeated with an almost perpendicular magnetic field. The model filamentary cloud is formed by fragmentation of a magnetized sheetlike cloud. It stays in a quasi-static equilibrium for a period that is much longer than its free-fall time. In the quasi-static equilibrium, the magnetic field runs parallel to the cloud axis in the central part of the cloud and almost perpendicular to the axis in the less dense part of the cloud. The inner parallel magnetic field supports the cloud in part against the cloud gravity. The parallel magnetic field escapes from the cloud through the Alfven wave and the quasistatic equilibrium state ends. During the quasi-static equilibrium, the cloud is expected to fragment in the direction of the axis by gravitational instability. We discuss the application of our model to the filamentary clouds in Taurus.