The orbit and fundamental physical parameters of the double-lined eclipsing binary V505 Per are derived by means of Echelle high resolution, high S/N spectroscopy and B, V photometry. Effective temperatures, gravities, rotational velocities and metallicities are obtained from atmospheric chi^2 analysis. An E(B-V)<=0.01 mag reddening is derived from interstellar NaI and KI lines. The distance to the system computed from orbital parameters (60.6 +/- 1 pc) is identical to the newly re-reduced Hipparcos parallax (61.5 +/- 1.9 pc). The masses of the two components (M(1) = 1.2693 +/- 0.0011 and M(2) = 1.2514 +/- 0.0012 Msun) place them in the transition region between convective and radiative stellar cores of the HR diagram, with the more massive of the two showing already the effect of evolution within the Main Sequence band (T(1) = 6512 +/- 21 K, T(2) = 6462 +/- 12 K, R(1) = 1.287 +/- 0.014, R(2) = 1.266 +/- 0.013 Rsun). This makes this system of particular relevance to theoretical stellar models, as a test on the overshooting. We compare the firm observational results for V505 Per component stars with the predictions of various libraries of theoretical stellar models (BaSTI, Padova, Granada, Yonsei-Yale, Victoria-Regina) as well as BaSTI models computed specifically for the masses and chemical abundances of V505 Per. We found that the overshooting at the masses of V505 Per component stars is already pretty low, but not null, and described by efficiencies lambda(OV)=0.093 and 0.087 for the 1.27 and 1.25 Msun components, respectively. According to the computed BaSTI models, the age of the system is about 0.9 Gyr and the element diffusion during this time has reduced the surface metallicity from the initial [M/H]=-0.03 to the current [M/H]=-0.13, in excellent agreement with observed [M/H]=-0.12 +/- 0.03.