A Linear Approximated Almost Ideal Demand System (LA/AIDS),used  to estimate the demand relationship for major food groups (cereals, beans ,meats ,fish, egg, milk, oil and sugar) in desert governorates in Egypt from 1990 – 2010.  Own-price, cross-price and expenditure elasticities were estimated  . The results of the analysis of food expenditure  elasticities of demand for different food groups showed that expenditure elasticities for all food groups were positive and less than one except for meats and milk groups which imply that it is a luxury good rather than other necessary good in the system. The results showed that the Marshallian own-price elasticities  was the highest for  meat group ,then sugar group, followed by oil, cereals , beans respectively then fish and milk ,and finally egg group  . On the other hand, the cross-price elasticities of oil  showed a complementary relationship with the other food groups.  There is a high substitutive relationship between beans and meats group, and between meats and fish groups. Compensated own-price elasticity estimates show similar trends but smaller values than uncompensated ones, which is theoretically consistent.