We used Optical, Near Infrared photometry and radial velocity data for a sample of 11 Cepheids belonging to the young LMC blue populous cluster NGC 1866 to estimate their radii and distances on the basis of the CORS Baade-Wesselink method. This technique, based on an accurate calibration of the surface brightness as a function of (U-B), (V-K) colors, allows us to estimate, simultaneously, the linear radius and the angular diameter of Cepheid variables, and consequently to derive their distance. A rigorous error estimate on radius and distances was derived by using Monte Carlo simulations. Our analysis gives a distance modulus for NGC 1866 of 18.51+/-0.03 mag, which is in agreement with several independent results. ; Comment: 21 pages, 10 figures, Accepted for publication in the Astrophysical Journal