Large pieces of paper-thin PLLA membranes are prepared and characterized as single-layered hollow fibrous assemblies with an extremely high degree of fiber alignment. The diameter of the electrospun hollow fibers is in the range of some tens of micrometers with a wall thickness of a few micrometers. They are best described as 2D arrays of highly aligned microtubes. The mechanical properties of the membranes are studied. A processing map is constructed using the applied electric field strength and the concentration (viscosity) of the electrospinning dope. The influence of factors such as the field strength and weight and viscosity of the jetted solutions is discussed. The results will help in the future fabrication of highly anisotropic scaffolds for tissue engineering applications.