Multi-lumen catheter having a monolithic elongate tubular shaft member having a proximal end, a distal end and a longitudinal length therebetween. The tubular shaft member has an outer cross-sectional dimension that varies along the length of the tubular shaft member. The tubular shaft member has an inner core made of a first material and an outer layer made of a second material. The inner core has a first lumen and a second lumen defined therein, the first lumen having a first lumen cross-section and a length extending at least along a portion of the length of the tubular shaft member. The first lumen cross-section is substantially uniform along the length of the first lumen. The second lumen has a second lumen cross-section and a length extending along the length of tubular shaft member. The second lumen cross-section is substantially uniform along the length of the second lumen.