This article reports the electrospinning technique for the manufacturing of multilayered scaffolds for bile duct tissue engineering based on an inner layer of polycaprolactone (PCL) and an outer layer either of a copolymer of D,L-lactide and glycolide (PLGA) or a copolymer of L-lactide and ε-caprolactone (PLCL). A study of the degradation properties of separate polymers showed that flat PCL samples exhibited the highest resistance to hydrolysis in comparison with PLGA and PLCL. Irrespective of the liquid-phase nature, no significant mass loss of PCL samples was found in 140 days of incubation. The PLCL- and PLGA-based flat samples were more prone to hydrolysis within the same period of time, which was confirmed by the increased loss of mass and a significant reduction of weight-average molecular mass. The study of the mechanical properties of developed multi-layered tubular scaffolds revealed that their strength in the longitudinal and transverse directions was comparable with the values measured for a decellularized bile duct. The strength of three-layered scaffolds declined significantly because of the active degradation of the outer layer made of PLGA. The strength of scaffolds with the PLCL outer layer deteriorated much less with time, both in the axial (p-value = 0.0016) and radial (p-value = 0.0022) directions. A novel method for assessment of the physiological relevance of synthetic scaffolds was developed and named the phase space approach for assessment of physiological relevance. Two-dimensional phase space (elongation modulus and tensile strength) was used for the assessment and visualization of the physiological relevance of scaffolds for bile duct bioengineering. In conclusion, the design of scaffolds for the creation of physiologically relevant tissue-engineered bile ducts should be based not only on biodegradation properties but also on the biomechanical time-related behavior of various compositions of polymers and copolymers.