This paper improves genetic programming (GP) and weight genetic programming (WGP) and proposes soft-computing polynomials (SCP) for accurate prediction and visible polynomials. The proposed genetic programming system (GPS) comprises GP, WGP and SCP. To represent confined compressive strength and strain of circular concrete columns in meaningful representations, this paper conducts sensitivity analysis and applies pruning techniques. Analytical results demonstrate that all proposed models perform well in achieving good accuracy and visible formulas; notably, SCP can model problems in polynomial forms. Finally, concrete compressive strength and lateral steel ratio are identified as important to both confined compressive strength and strain of circular concrete columns. By using the suggested formulas, calculations are more accurate than those of analytical models. Moreover, a formula is applied for confined compressive strength based on current data and achieves accuracy comparable to that of neural networks.