To understand the characteristics of the plasma sheath within small tubes, a two-dimensional numerical model of helium discharge within dielectric tubes is developed. During the plasma propagation for the tube diameter of 0.05 mm, the sheath thickness in the plasma head is almost equal to the tube radius. It decreases rapidly to several micrometers at the axial distance of 0.05 mm behind the plasma head, and then slightly increases and saturates at the axial position far behind the plasma head. A plasma-gas sheath surrounding the central plasma column is observed for the tube diameter equal to or greater than 0.8 mm. It is replaced by a plasma-wall sheath for smaller tubes. With the decrease of the tube diameter, the sheath thickness far behind the plasma head decreases and while the ion flux increases significantly. On the other hand, when the O2 gas with a proportion of 2% is added, both the sheath thickness and the ion flux decrease.