  We theoretically investigate pairing states of the spin-triplet p-wave
superfluid 3He confined in narrow cylinders. The surface-induced distortion and
the multiple internal degrees of freedom of the order parameter lead to the
occurrence of a stripe structure along the cylinder axis in the superfluid
3He-B phase. We show that in sufficiently small cylinders with an anisotropic
surface scattering, the stripe order with broken translational symmetry may be
stabilized as the lowest energy state. Periodic spin-current textures caused in
this inhomogeneous superfluid phase are also discussed.
