Embodiments of an expandable sheath can be used in conjunction with a catheter assembly to introduce a prosthetic device, such as a tissue heart valve, into a patient. Such embodiments can minimize trauma to the vessel by allowing for temporary expansion of a portion of the introducer sheath to accommodate the delivery apparatus, followed by a return to the original diameter once the prosthetic device passes through. Some embodiments can comprise a sheath with inner and outer tubular layers, and an intermediate tubular layer comprising a shape memory alloy. Other embodiments comprise one or more layers having one or more longitudinal notches or cuts to facilitate expansion of the sheath. Embodiments of the present expandable sheath can avoid the need for multiple insertions for the dilation of the vessel, thus offering advantages over prior art introducer sheaths.