Poly(glycerol sebacate) (PGS) is a biocompatible, biodegradable elastomer that has been shown promise as a scaffolding material for tissue engineering; it is still challenging, however, to produce anisotropic scaffolds by using a thermoset polymer, such as PGS. Previously, we have used aligned sacrificial poly(vinyl alcohol) (PVA) fibers to help produce an anisotropic PGS membrane; a composite membrane, formed by embedding aligned PVA fibers in PGS prepolymer, was subjected to curing and subsequent PVA removal, resulting in aligned grooves and cylindrical pores on the surface of and within the membrane, respectively. PVA, however, appeared to react with PGS during its curing, altering the mechanical characteristics of PGS. In this study, aligned sacrificial fibers made of polylactide (PLA) were used instead. Specifically, PLA was blend-electrospun with polyethylene oxide to increase the sacrificial fiber diameter, which in turn increased the size of the grooves and cylindrical pores. The resultant PGS membrane was shown to be in vitro cyto-compatible and mechanically anisotropic. The membrane's Young's modulus was 1-2 MPa, similar to many soft tissues. In particular, the microscale grooves on the membrane surface were found to be capable of directing cell alignment. Finally, based on the same approach, we fabricated a biomimetic, anisotropic, PGS tubular scaffold. The compliance of the tubular scaffold was comparable to native arteries and in the range of 2% to 8% per 100 mmHg, depending on the orientations of the sacrificial fibers. The anisotropic PGS tubular scaffolds can potentially be used in vascular tissue engineering.