Although some official statements have been released by the Federal Emergency Management Agency (FEMA) and the National Institute of Standards and Technology (NIST), the 9/11 tragedy of the New York World Trade Center (WTC) towers still remains as an unresolved mystery since the progressive collapse sequence of the towers was unnaturally rapid. We sought the true cause of the collapse by performing full-model, dynamic collapse analyses of the WTC towers due to aircraft collision. The numerical code used in the analyses is based on the ASI-Gauss technique, a modified version of the formerly developed adaptively shifted integration (ASI) technique, which computes highly accurate elastoplastic solutions even with the minimum number of elements per member. The ASI-Gauss technique gains still a higher accuracy particularly in the elastic range, by placing the numerical integration points of the two consecutive elements forming an elastically deformed member in such a way that stresses and strains are evaluated at the Gaussian integration points of the two-element member. Moreover, the technique can be used to express member fracture, by shifting the numerical integration point to an appropriate position and by releasing the resultant forces in the element simultaneously. The numerical results show instant disconnections between the core columns and the main double trusses during the impact, and a spring-back phenomenon of the core columns due to a very rapid unloading is observed. The spring-back phenomenon is fatal enough to produce a gigantic tensile force on the columns, which might have triggered the total fracture of some connections, eventually leading to the total collapse of the towers.