An inflatable evacuation slide (12) for emergency evacuation of an aircraft (16) comprises a pair of main support tubes (24,28) supporting a flexible sliding surface (30). The main support tubes (24,28) taper from a widest point near the exit opening of the aircraft (16) to a narrowest point at the foot end (50) of the slide (12). This arrangement of main support tubes (24,28), together with the toe end transverse tube (54) and the head end transverse tube (56), form a quasi-trapezoidal truss structure, which is inherently more stable than the rectangular slides of the prior art.