We present a quantitative morphological analysis using Hubble Space Telescope ( HST ) NICMOS H _ { 160 } - and ACS I _ { 775 } -band imaging of 25 spectroscopically confirmed submillimetre galaxies ( SMGs ) which have redshifts between z = 0.7 –3.4 ( \bar { z } = 2.1 ) . Our analysis also employs a comparison sample of more typical star-forming galaxies at similar redshifts ( such as Lyman Break Galaxies ) which have lower far-infrared luminosities . This is the first large-scale study of the morphologies of SMGs in the near-infrared at \sim 0.1 ^ { \prime \prime } resolution ( \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle < $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 1 kpc ) . We find that the half light radii of the SMGs ( r _ { h } =2.3 \pm 0.3 and 2.8 \pm 0.4 kpc in the observed I - and H -bands respectively ) and asymmetries are not statistically distinct from the comparison sample of star-forming galaxies . However , we demonstrate that the SMG morphologies differ more between the rest-frame UV and optical-bands than typical star-forming galaxies and interpret this as evidence for structured dust obscuration . We show that the composite observed H -band light profile of SMGs is better fit with a high Sersic index ( n \sim 2 ) than with an exponential disk suggesting the stellar structure of SMGs is best described by a spheroid/elliptical galaxy light distribution . We also compare the sizes and stellar masses of SMGs to local and high-redshift populations , and find that the SMGs have stellar densities which are comparable ( or slightly larger ) than local early-type galaxies , but comparable to luminous , red and dense galaxies at z \sim 1.5 which have been proposed as direct SMG descendants , although the SMG stellar masses and sizes are systematically larger . Overall , our results suggest that the physical processes occuring within the galaxies are too complex to be simply characterised by the rest-frame UV/optical morphologies which appear to be essentially decoupled from all other observables , such as bolometric luminosity , stellar or dynamical mass .