Quantities of oranges exports represents about 11.3% from the total domestic production, also value of oranges exports represents about 7.3% from the total agricultural experts as an average to the period (1987-2004). Although the British market is considered a traditional markets in importing the Egyptian oranges. but the quantities exported from Egypt does not suitable with the whole British importation of oranges. The problem of this study and the objective are concerned with estimating the British demand on the Egyptian oranges exports. and standing on the nature of the relations among export prices of the competing countries that export oranges to the United Kingdom. The study estimated Armington demand system on the British imports of oranges. by seemingly unrelated regression procedure (SUR), also the assumptions of adding up, homogeneity, and symmetry, were included as restrictions in the demand system. The Data of the study covered the pen'od subject to study (1937-2004). Armington demand system considered that, Egypt, Spain, Israel, Morocco, are competing countries in exporting oranges to the British market, where contribute by about 5.36%, 51.63%, 20.75%, 21.74% from their total exported quantities, and about 3.05%, 59.11%, 19.41%, 18.43% from their total value of exports to the United Kingdom respectively. Results of Armington model showed that, the Spanish market competes the Egyptian exports of oranges to United Kingdom, and lead to decrease the demand on oranges from Egypt. Finally, the study recommended by integrated strategy starting from special oranges production for exporting, and creating new international markets in the world, and decrease the import tariffs on production inputs to decrease the costs of production.