Abstract: The calculation of bearing capacity of foundations is a fundamental topic in soil mechanics. However, the contribution of the unit weight of the foundation soil to the bearing capacity cannot yet be satisfactorily calculated. The fundamental reason is that this part of bearing capacity is actually not independent, and consequently cannot be calculated separately. In order to study the mechanism of foundation bearing capacity and the relevant theory thoroughly, it is first revealed that the surcharge load corresponding to footing embedment and the unit weight of the foundation soil, multiplied by the soil strength parameter\tan \varphi , can be treated respectively as the equivalent cohesion and the rate of cohesion increase along depth. Then a new method is developed for the general failure mode of strip footing under non-eccentric vertical loads. In this new method a non-dimensional parameter is defined to well reflect the influences of the soil strength and soil weight on the bearing capacity, and based on which a unified formula for the calculation of bearing capacity is established, in which the soil strength, the embedment depth of the footing and the soil weight are all considered as closely related elements. For the bearing capacity of foundation under other more complicated conditions, such as failure in local mode, different footing shapes, inclined loads etc., the available methods of treatment can be still applied in combination with the newly developed formula. Careful comparison with the refined numerical calculations proves the reliability and high accuracy of the proposed formula, and at the same time it proves the rationality and correctness of the whole idea as well as the constructed non-dimensional parameter. Besides, comparisons are also made with the formulas by Terzaghi and Hansen to show the significant improvement of the proposed method over the formers.