Likely radii for the inner and outer Lindblad resonances (ILR, OLR), the corotation resonance (CR), the inner 6:1 and 4:1 resonances, and the outer 1:1 resonance in the grand design galaxy NGC 1566 are identified from optical features and from constraints set by plausible rotation curves. In the preferred solution, the OLR is placed where the outer edge of the spiral pattern joins the outer ring, the CR is at the endpoints of the bright star-formation ridges and sharply defined dust lanes, where the main arms bifurcate and a ring of interarm star-formation circles the galaxy, the 6:1 resonance is where two short and faint spurs lie parallel and equally spaced between the main arms in the west, the 4:1 resonance is where a large and bright spur lies midway between the arms in the east and where there is a kink in both arms, and the ILR is at the position of another kink in the spiral at the inner part of the galaxy, near the end of a small bar. The outer ring extends between the OLR and the outer 1:1 resonance. The ratios of these resonance radii to the corotation resonance are shown to be relatively insensitive to the rotation curve, and all of the observed ratios are in good agreement with theory. Other possible solutions for the resonance radii are discussed.