Introducer sheath for use in inserting a balloon catheter into a patients vasculature includes a tubular member having an inner diameter, an outer diameter, a proximal end, a distal end, and a length therebetween, the inner diameter being sized to receive a catheter shaft having an attached expandable member in a deflated condition. The inner diameter can be varied from a first inner diameter at the proximal end and a second inner diameter at the distal end, the first inner diameter being greater than the second inner diameter. A method of inserting a balloon catheter into the vasculature of a patient is also disclosed. Additionally, a balloon catheter kit including a catheter and an introducer sheath is disclosed.
