The unified hardening model for clays and sands (CSUH) can adequately represent the stress-strain characteristics of various soil types. However, being an incremental elastoplastic constitutive model, the CSUH model requires extensive iterative computations during parameter identification, resulting in significant computational time. To improve computational efficiency, this study derives the elastoplastic compliance matrix and stress-strain incremental relationships under different stress paths, eliminating the repeated solving of equations typically required during iterative processes. Furthermore, a dynamic step size iterative method is proposed based on the changing slope characteristics of the stress-strain curves. This method divides the total axial strain into two segments: in the initial segment (approximately the first 30% of total strain), where the curve slope is steep, smaller step sizes with arithmetic progression distribution are employed, while in the latter segment (approximately the remaining 70%), characterized by a gentle curve slope, larger and uniformly distributed step sizes are adopted. Comparative analyses between the proposed dynamic step size method and the traditional constant-step iterative method demonstrate that, under the premise of ensuring calculation accuracy, the dynamic step size method significantly reduces the iteration steps from 3000 to 50, thus decreasing the computational time by approximately 47 times. Finally, the proposed method is applied to parameter identification of Fujinomori clay, calcareous sand, and Changhe dam rockfill materials using the CSUH model. The predictions closely match experimental results, confirming the CSUH model's capability in accurately describing the mechanical behaviors of different soils under various stress paths. The dynamic step size iterative approach developed in this study also provides valuable insights for enhancing computational efficiency and parameter identification of other elastoplastic constitutive models.