Sand contaminated with sulphates is a local problem in the Middle East Area. It is difficult to obtain well graded sand with sulphate content within the limits specified by international standards. International standard adopt different concepts in limiting internal SO3 contents in concrete. Some standards put maximum limits for SO3 by weight of aggregate only, other standards, limit the total SO3 in concrete by weight of cement in the concrete, while surprisingly a third group has no limitation on internal SO3 in concrete. In this research work, an attempt was made to study the possibility of adopting the second concept only (total SO3 in concrete by weight of cement) and overlook all other concepts, as it reasonably provides a complete picture of the presence of sulphates in the concrete mix. This work focuses only on internal sulphate attack, and investigates different concrete mixes with compressive strengths between 15 and 75 MPa. In these mixes sand with SO3 between 0.5% and 2.0% was used, thus yielding total SO3 contents by weight of cement in the range of 3.2–10.5%. Two important properties concerning sulphate attack were studied; these were; compressive strength and expansion in water up to 180 days. From the results obtained, it was found that increasing the concrete compressive strength, resulted in increasing its resistance to internal sulphate attack, and concrete mixes with high strength (>45 MPa) had almost the same expansion in water, despite the increase in the sulphate content in the sand from 0.5% to 2.0%. As a result of this work, it was clear that it is better to specify total sulphates in concrete as a percent by weight of cement, rather than limiting sulphates in aggregates as specified in some international standards. Based on the present results, it was concluded that new values of total SO3 content in concrete by weight of cement can be specified at 6.0%, 5.5% and 5.0% for concrete mixes with cement contents <400, 400–500 and above 500 kg/m3 respectively regardless to SO3 contents in the aggregates.