To estimate the traffic loading on long span bridges two independent statistical techniques were developed. One was purely analytical, the other used a computer to generate random" traffic" and calculate the maximum load on the bridge. The two methods gave remarkably similar results. Further research produced not only maximum loads, but also maximum moments and shears. From this work the following results emerge: With a knowledge of the average mix of traffic, a design loading can be estimated with a good degree of confidence using the techniques developed. The loading can be accurately represented by a uniform load and a concentrated load in the traditional manner. Unlike the AASHO loading, one set of uniform and concentrated loads can be used to represent both maximum moment and maximum shear. As expected, the uniform load per foot reduces as the loaded length is increased. Unlike AASHO and previous assumptions, it is found that the concentrated load increases as the loaded length increases. When several lanes are loaded simultaneously they do not, as suggested by AASHTO, all carry the same load. A simple distribution formula has been found. These results have significant implications for the designers of long span bridges; and typical results have been produced for various types of traffic./Author/