The in vitro responses of Schwann cells (RT4-D6P2T, a schwannoma cell line derived from a chemically induced rat peripheral neurotumor) on various types of electrospun fibrous scaffolds of some commercially available biocompatible and biodegradable polymers, i.e., poly(3-hydroxybutyrate) (PHB), poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV), polycaprolactone (PCL), poly(L-lactic acid) (PLLA), and chitosan (CS), were reported in comparison with those of the cells on corresponding solution-cast film scaffolds as well as on a tissue-culture polystyrene plate (TCPS), used as the positive control. At 24 h after cell seeding, the viability of the attached cells on the various substrates could be ranked as follows: PCL film > TCPS > PCL fibrous > PLLA fibrous > PHBV film > CS fibrous approximate to CS film approximate to PLLA film > PHB film > PHBV fibrous > PHB fibrous. At day 3 of cell culture, the viability of the proliferated cells on the various substrates could be ranked as follows: TCPS > PHBV film > PLLA film > PCL film > PLLA fibrous > PHB film approximate to PCL fibrous > CS fibrous > CS film > PHB fibrous > PHBV fibrous. At similar to 8 h after cell seeding, the cells on the flat surfaces of all of the film scaffolds and that of the PCL nanofibrous scaffold appeared in their characteristic spindle shape, while those on the surfaces of the PHB, PHBV, and PLLA macrofibrous scaffolds also appeared in their characteristic spindle shape, but with the cells being able to penetrate to the inner side of the scaffolds.