Using two different test standards (ASTM and BS), the influence of five different sizes of sand on the ultimate stress (MPa) of hand-mixed cement-grouted sands modified with polymer is discussed in this study. The characteristics of cement-grouted sands modified with polymer up to 0.16% (percent weight of dry cement) were evaluated and measured in fresh and hardened conditions. Adding polymer decreased the water/cement ratio ( w∕c ) from 0.6 to 0.5, and it kept the flow time of the cement-based grout in the range of 18 to 23 s recommended by ASTM standard. Using mix proportion and curing time, adding polymer significantly increased the prismatic and cylindrical compressive strength (MPa) by 113 to 577% and 53 to 459%. Several mathematical approaches such as linear regression (LR), Nonlinear regression (NLR), multilinear regression (MLR), Artificial neural network (ANN), and M5P-tree were used to predict the compression strength of cement-grouted sand with a different size of sand, w/c, polymer content, and curing age. Based on the scatter index (SI), objective function (OBJ) assessments, and training and testing datasets, the compressive strength of the cement-grouted sands can be predicted well using NLR and ANN models. The compression strength tested using the BS standard was 71% higher than the compression strength of the same mix tested using the ASTM standard.