This paper focuses on the application of two dimensional orthogonal polynomials in the regression analysis for the relationship of product parameters viz. compressive strength, bulk density and water absorption of fly ash cement bricks with other process parameters such as percentages of fly ash, sand and cement. The method has been validated by linear and non-linear two parameter regression models. The use of two dimensional orthogonal system makes the analysis computationally efficient, simple and straight forward. Corresponding co-efficient of determination and F-test are also reported to show the efficacy and reliability of the relationships. By applying the evolved relationships, the product parameters of fly ash cement bricks may be approximated for the use in construction sectors.