This paper presents an experimental and numerical study of a pulsed air plasma discharge at atmospheric pressure propagating in a capillary glass tube. In this work, we have compared the discharge structures and the axial propagation velocities of discharges. First, we have studied a needle-to-plane configuration without tube. For applied voltages in the range 7-18 kV, we have observed in experiments and in simulations that a plasma ball starts to develop around the needle tip. Then, for applied voltages less than 14 kV, in experiments, the discharge rapidly splits into several streamer channels with a main axial streamer. In simulations, we have computed only the main axial discharge. For applied voltages higher than 14 kV, in experiments and in simulations, we have observed that the discharge propagates with a cone shape in the gap. For all studied voltages, a good experiment/modelling agreement is obtained on the axial propagation velocity of the discharge, which increases with the applied voltage. Then, we have studied the propagation of discharges inside capillary tubes with radii in the range 37.5-300 μm. In experiments and simulations, we have observed that for small tube radius, the discharge front is quite homogeneous inside the tube and becomes tubular when the tube radius increases. Experimentally, we have observed that the velocity of the discharge reaches a maximum for a tube radius slightly less than 100 μm. We have noted that for a tube radius of 100 μm, the discharge velocity is three to four times higher than the velocity obtained without tube. This clearly shows the influence of the confinement by a capillary tube on the discharge dynamics. In this work, we have only simulated discharges for tube radii in the range 100-300 μm. We have noted that both in experiments and in simulations, the velocity of the discharge in tubes increases linearly with the applied voltage. As the radius of the tube decreases, the discharge velocity derived from the simulations slightly increases but is less than the experimental one. We have noted that the discrepancy on the discharge velocity between experiments and simulations increases as the voltage increases.