The velodrome, first of the structures to be completed for the 1976 Olympic Games in Montreal, posed unusual construction problems involving site precasting, post-tensioning, and finally decentering the vast arches that comprise the principal roof supports. The 18,000 square foot shield shaped roof is made up of three lobes- geometrically described as lunes- bounded by spherical, flattened arches with a clear span of nearly 560 feet. Three pairs of these concrete arches, rising to a maximum elevation of 110 feet, support the 41,000 ton roof load. The arch ribs which fan out form a single abutment to three supports on the opposite side were built from a total of 144 segments, 20 feet long, precast at the site in a yard adjacent to the velodrome. The builder used 7 sets of forms to produce the several shapes of arch segments needed. Casting each segment required more than 4 days: 2 days for erecting forms and setting reinforcing steel in place, 3 hours for placing concrete, and 48 hours for curing. Each completed segment was placed on its own cradle-like frame that positioned it at the precise inclination it would have in the completed arch. As soon as the major arches were assembled in position on the scaffolding, the transverse roof members comprising a lattice of double-Y shaped precast pieces were hoisted into place and joined to the arches at their stems by post-tensioning tendons. Most of the roof over the Y-shaped segments was covered with translucent skylights, and a few sections of concrete were cast in place near the pints of convergence of the arches to complete the roof. When the post-tensioning of the arches was about 80 percent complete, the contractor faced the challenge of decentering. Because of the complexity of both the structure and the operation, a computer program was set up for tridimensional computation, using finite element analysis to determine the proper amount and sequence of forces to be applied.