This study aims to perform experiments to determine both initial shear modulus and unconfined compressive strength of Bangkok soft clay improved by the ordinary Portland cement (OPC) and fly ash (FA). The role of cement is for stabilizing Bangkok soft clay, whereas the cement replacement by FA is for sustainable purpose because FA is a waste by-product from the Mae Moh power plant in Thailand. The Bangkok soft clay is mixed with OPC of 20% by weight as well as FA replacement of 0–30% by weight. After curing for 7, 14, 28 and 90 days, the initial shear modulus is determined from shear wave velocity measured by a self-developed non-destructive bender element, which is appropriate for cyclically and continuously curing time modelling. For comparisons and result validation, the strength development of tested clay samples is also determined by the destructive unconfined compressive strength (UCS) tests. From the study, the initial shear modulus reveals the optimum FA replacement of 20% at 90 days, whereas the unconfined compressive strength reveals that of 15% at 90 days. Moreover, both the initial shear modulus and the unconfined compressive strength increases with the curing time. The relationship between the normalized unconfined compressive strength and the curing time is found as naturally logarithmic with the increase rate at 0.3433, and the early-age normalized unconfined compressive strength is found as 0.09. By comparison with a study, the limitation of the bender element tests is found, as only the small strain quantity in terms of G0 or E can be determined in spite of being beneficial for constitutive modelling in various computations (e.g., the finite element method, FEM, dynamic analysis of soil property, etc.). The relationship between normalized shear modulus and unconfined compressive strength in this study agrees with other studies, but some discrepancy exists due to different compositions, clay type, cement content, and stabilizers. Thus, further studies on this discrepancy are recommended.