Large civil structures such as bridges must be permanently monitored to ensure integrity and avoid collapses due to damage resulting in devastating human fatalities and economic losses. In this article, a wavelet-based method called the Wavelet Energy Accumulation Method (WEAM) is developed in order to detect, locate and quantify damage in vehicular bridges. The WEAM consists of measuring the vibration signals on different points along the bridge while a vehicle crosses it, then those signals and the corresponding ones of the healthy bridge are subtracted and the Continuous Wavelet Transform (CWT) is applied on both, the healthy and the subtracted signals, to obtain the corresponding diagrams, which provide a clue about where the damage is located; then, the border effects must be eliminated. Finally, the Wavelet Energy (WE) is obtained by calculating the area under the curve along the selected range of scale for each point of the bridge deck. The energy of a healthy bridge is low and flat, whereas for a damaged bridge there is a WE accumulation at the damage location. The Rio Papaloapan Bridge (RPB) is considered for this research and the results obtained numerically and experimentally are very promissory to apply this method and avoid accidents.