In this study, electrospinning was used to prepare ultrafine fibers from PHAs with different chemical compositions: P(3HB) and copolymers: P(3HB-co-4HB), P(3HB-co-3HV), and P(3HB-co-3HHx). The main process parameters that influence ultrafine fiber diameter and properties (polymer concentration, solution feeding rate, working distance, and applied voltage) have been investigated and their effects evaluated. The study revealed electrospinning parameters for the production of high-quality ultrafine fibers and determined which parameters should be varied to tailor the properties of the products. This study is the first to compare biological and physical-mechanical parameters of PHAs with different chemical compositions as dependent upon the fractions of monomers constituting the polymers and ultrafine fiber orientation. Mechanical strength of aligned ultrafine fibers prepared from different PHAs is higher than that of randomly oriented ones; no significant effect of ultrafine fiber orientation on surface properties has been found. None of the fibrous scaffolds produced by electrospinning from PHAs had any adverse effects on attachment, growth, and viability of NIH 3T3 mouse fibroblast cells, and all of them were found to be suitable for tissue engineering applications.