The formation of birefringent structures inside nanoporous glass by femtosecond laser pulses was investigated. The laser-modified region is shown to be a cavity whose shape depends on the number of pulses. The shape of the void cross section varied from circle to ellipse when increasing the number of pulses from one to three. A layer of non-porous dense glass was revealed around the cavity. The cross section of this layer is nearly circular, regardless of the cavity shape and number of pulses in the investigated range. The mechanism of elongated cavity formation based on aniostropic light scattering on the spherical cavity is proposed.