The spectral phase shift of surface plasmon resonance (SPR) in the Kretschmann configuration is modeled for aqueous solutions of NaCl (analytes) and an SPR structure consisting of gold and chromium layers deposited on an SF10 glass slide. Using the material dispersion of the SPR structure and the analyte, the SPR phase shift, its spectral derivative, and the spectral dependence of the ratio of the reflectances of p- and s-polarized waves are determined for aqueous solutions of NaCl when the concentration of NaCl in water and the refractive index range from 0 to 10 weight percent (wt%) and from 1.3334 to 1.3515 RIU, respectively. In addition, theoretical modeling is accompanied by experiment and the position of a sharp maximum in the measured spectral derivative of the SPR phase shift changes in a range from 596 to 626 nm. From the measurements, a sensitivity to concentration of 3.83 nm/wt% and a detection limit of 7.3 × 10−7 RIU at a wavelength of 612.36 nm are obtained, and very good agreement between theory and experiment is confirmed.