Does cabinet shape affect bass response?

I've no idea why the shape of a cabinet would affect bass response. Volume is the only significant factor, right?
I ask this question because I've spent a lot of time trying fashion a subwoofer to fit under a bed. I think I'm currently embarking of MK VI.
Cabinet making is not my forte. So it's easier for to use a floor-standing tower cabinet as a base (25 litres). But on reflection I've never met a skinny floor-stander with an impressive bass response.
Has the shape got anything to do with it?
 
Absolutely and unreservedly yes. Non-cuboid shapes can push any panel resonances way out of the sub's pass band without the need for excessive bracing and panel damping. My undamped 15mm ply enclosures (18" 700W PA drivers and minimal volume damping) have their first significant panel resonance at over 500Hz. On a practical note, with sensible bracing a long flat enclosure will work adequately well, but don't expect significant output if you are using small drivers unless in multiples.
Move a lot of air - GENTLY!