In this talk we will describe the $\SU(3)$-structure induced on an oriented hypersurface of a 7-dimensional manifold with a nearly parallel $\G2$-structure. We call such $\rm{SU}(3)$-structures \textit{nearly half-flat}. We characterise the left invariant nearly half-flat structures on $S^3\times S^3$. This characterisation then help us to systematically analyse and give examples of nearly parallel $\G2$-structures on an interval times $ S^3\times S^3$.