Random walks (RWs) and nonreversal random walks (NRRWs) embedded in various lattices and freely jointed (off-lattice) chains-consisting of up to N almost-equal-to 1000 segments-have been produced and analyzed with respect to their instantaneous shape. While the results of different RWs (as expected) coincide for all chain-lengths examined, the short-chain behavior of NRRWs is strongly dependent on the lattice type. In the limit of infinitely long chains, however, quantities characteristic of the shape converge to common values for all types of RWs and NRRWs examined.