The Separation of two amino acids, phenylalanine and tryptophan, was carried out using laboratory simulated moving bed (SMB) chromatography. The SMB process consisted of four zones, with each zone having 2 columns. The triangle theory was used to obtain the operating conditions for the SMB. The mass transfer coefficients of the two amino acids were obtained from the best-fit values by comparing simulated and experimental pulse data. The competitive adsorption isotherms of the two amino acids were obtained by single and binary frontal analyses, taking into consideration the competition between the two components. A competitive Langmuir isotherm, obtained from single-component frontal chromatography, was used in the first run, and the isotherm from binary frontal chromatography in the second, with the flow rate of zone 1 modified to improve the purity. Compared to the first and second runs, the competitive Langmuir isotherm from the binary frontal chromatography Showed good agreement with the experimental results. Also, adjusting the flow rate in zone 1 increased the purity of the products. The purities of the phenylalanine in the raffinate and the tryptophan in the extract were 99.84 and $99.99\%$, respectively.