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A simple method is developed for predicting the fracture behaviour of structures made of quasi-brittle materials such as concrete and rock using the data from laboratory-sized specimens. The method is based on the recently-developed boundary effect concept and associated asymptotic model. It is demonstrated that the "apparent" size dependence of fracture behaviour of concrete and rock is in fact due to the influence of specimen boundaries. Various size effect phenomena that are often observed in fracture mechanics tests of concrete and rock are related to each other, and the asymptotic boundary effect model can explain all the observed "size" effect phenomena. Four types of experimental results available in the literature (including the data measured on (1) the specimens of identical size with different crack-to-size (α) ratios, (2) specimens of different sizes with different α-ratios, (3) different types of specimens and (4) geometrically similar specimens) are used to verify the asymptotic boundary effect model, and it is found that the predictions of the model agree very well with the experimental results. Furthermore, the important fracture properties, fracture toughness KIC and strength ft of quasi-brittle materials such as concrete and rock can also be calculated using the formulae provided in the model.