We have prepared a polydomain smectic liquid crystalline (LC) elastomer by introducing 2 mol % 1,3,5-benzenetricarboxylic acid as a cross-linker into a main-chain BB-5 polyester. The elastomer designated as BB-5/E2 forms isotropic and sinectic CA (SmCA) LC phases in order of decreasing temperature similarly to the un-cross-linked BB-5 polyester. BB-5/E2 in the isotropic liquid phase shows a typical rubberlike elasticity, whereas that in the SmCA phase shows a characteristic elongation behavior accompanying a polydomain-monodomain transition: the initial strain Lip to 100% orients the smectic layer with its normal parallel to the elongation direction, and the further elongation does not change the layer orientation and results in permanent deformation. The corresponding stress-strain Curve shows a quasi-plateau, which is a so-called "soft stress plateau over a wide strain region from 100% to 450%. These indicate that the polymer chains folded in the oriented smectic LC elastomer at a strain of 100% are stretched oil further elongation and locked by the sinectic layer order. At a strain of more than 300%, the SmCA phase begins to transform into a crystal because of the entropy reduction due to direct stress to the fully extended polymer chains.