The Rotterdam and the almost ideal demand systems (AIDS) are often used to model consumer demand system. The present study determined which model performed better in recovering the true elasticities of consumer demand for red meat and fish. For the linearised AIDS model, Stone, Paasche, Laspeyres, and Turnquist price indexes were used. This study also compared the results of the linearised AIDS and the full nonlinear AIDS (NLAIDS) models. According to Lutkepohl, normality test for joint residuals, the linearised AIDS model that used Turnquist price index, was the best system and, based on the Akaike criteria, the linear approximate (LA) AIDS outperformed NLAIDS. The results of the non-nested test for LAAIDS versus Rotterdam showed that LAAIDS is more appropriate for red meat and fish demand in Iran. Price elasticity for fish and red meat showed that they are elastic. Cross elasticity from LAAIDS and NLAIDS showed that fish and red meat are substitutes. Allen-Uzawa elasticity results indicate that the two goods are strong substitutes. Income elasticity indicated that red meat and fish are considered to be luxury goods.