The shape of unperturbed polymer chains was studied using the Monte Carlo technique on a tetrahedral lattice.The asphericity A, the ratios <L22>/<L12> and <L32>/<L12> were calculated for different values of polymer chain length n,conformational energy ε (ε≥ 0) and temperature T. The asphericity A decreases with the increase of chain length and tends to reach its limiting value rapidly with the decrease of γ (γ = ε/kBT). For large n, A is about 0.525 ± 0.005, the ratios<L22>/<L12> and <L32>/<L12> are about 2.7 and 12.0, respectively, and are almost independent of γ, but for short chains, they depend on γ.