The structural, electronic, optical and vibrational properties of the collapsed (10,10) single-walled carbon nanotube bundle under hydrostatic pressure have been studied by the first-principles calculations. Some features are observed in the present study: First, a collapsed structure is found, which is distinct from both of the herringbone and parallel structures obtained previously. Secondly, a pseudo-gap induced by the collapse appears along the symmetry axis textit{$Gamma $X}. Thirdly, the relative orientation between the collapsed tubes has an important effect on their electronic, optical and vibrational properties, which provides an efficient experimental method to distinguish unambiguously three different collapsed structures.