The problem investigated in this research is that engineering design decision making can be complicated and made difficult by highly coupled design parameters and the vast number of design parameters. This complication often hinders the full exploration of a design solution space in order to generate optimal design solution. These hindrances result in inferior or unfit design solutions generated for a given design problem due to a lack of understanding of both the problem and the solution space. This research introduces a computational framework of a new algebraic constraint-based design approach aimed at providing a deeper understanding of the design problem and enabling the designers to gain insights to the dynamic solution space and the problem. This will enable designers to make informed decisions based on the insights derived from parameter relationships extracted. This paper also describes an enhanced understanding of an engineering design process as a constraint centered design. It argues that with more effort and appreciation of the benefits derived from this constraint-based design approach, engineering design can be advanced significantly by first generating a more quantitative product design specification and then using these quantitative statements as the basis for constraint-based rigorous design. The approach has been investigated in the context of whole product life-cycle design and multidisciplinary design, aiming to derive a generic constraint-based design approach that can cope with life-cycle design and different engineering disciplines. A prototype system has been implemented based on a constraint-based system architecture. The paper gives details of the constraint-based design process through illustrating a worked real design example. The successful application of the approach in two highly coupled engineering design problems and the evaluation undertaken by a group of experienced designers show that the approach does provide the designers with insights for better exploration, enabled by the algebraic constraint solver. The approach thus provides a significant step towards fuller scale constraint-based scientific design.