We present our searches for the tubular bound states of a D2-brane with m D0-branes and n fundamental strings in the NS5-brane, Dp-brane or macroscopic strings background by solving the Dirac-Born-Infeld equation. The geometry of tubular configurations we considered are taken to be parallel to the background branes or macroscopic strings. The n fundamental strings therein may be the circular strings F_c or the straight strings F_s, which are along the cross section or the axis of the tube respectively. We show that the stable tubular bound states of (nF_s, mD0, D2) which are prevented form collapse by the angular momentum, as original found in flat space, could be formed in the NS5-brane, D6-brane and macroscopic strings background. However, they becomes unstable in the D2-brane and D4-brane background. We also show that there are stable tubular bound states of (nF_c, mD0, D2) and (mD0, D2), which are prevented form collapse by the gravitational forces in the backgrounds of D6-brane. We discuss the properties of these tubular solutions and see that only that in the macroscopic strings background is a supersymmetric BPS configuration.