The strength of high strength concrete (HSC) produced from binary and ternary binders was investigated experimentally and a modelling study was done. Binary blends were composed of Portland cement (PC) + silica fume (SF) or white portland cement (WPC) + high reactivity metakaolin (HRMK). Some of the ternary blends contained PC, SF and a third binder which was either fly ash class F (FA/F), or class C (FA/C), or ground granulated blastfumace slag (S). Some others contained WPC, HRMK and ground pumice (P). The HSC samples were prepared in laboratory by varying the total binder content and binder type. The experimental results show that, in the case of concretes from binary binders, SF and HRMK used in proper amounts caused the significantly increase of strength. FA/F, FA/C and S, as a third binder in ternary blends, also increased strength whereas P addition does not contribute to the strength increase in white concrete from WPC and HRMK. Three methods were used to predict some of the measured experimentally strength. There are: artificial neural network (ANN), multiple linear regression analysis (MLR) and nonlinear multiple regression analysis (NLMR). The accuracy of prediction was tested by error analyses. It was found that the strength of the concrete samples can be successfully predicted by all three methods. However, ANN and NLMR gave comparable results and predicted the strength better than MLR, especially for the ternary binders.