To experimentally determine the multidirectional driving point and transfer accelerance matrices is a difficult task that has remained unsolved for 30 years. These matrices relate both linear and rotational degrees of freedom in three dimensions. The direct measurement of dynamic moments and rotational accelerations is very difficult. Little work exists on the subject and none includes so many DOF's. Besides, it is assumed that any test attachment is rigid and none used angular accelerometers to measure the angular acceleration;Various errors in substructure testing are studied. The study reveals that the interface DOF deficiency error is the most catastrophic and sophisticated error. None of interfacial DOF's can be neglected. The bias error can be corrected easily. The noise error appears to be most severe in the low frequency range. The exciter rocking motion leads to incorrect bare vehicle transmissibility matrix and incorrect global transmissibility matrix. The driving point difference error increases quickly as the distance between the impact and measurement points increases;The DOF deficiency error has several sources. It comes from the difference between the inverse from a complete interface model and the inverse of a reduced interface model. It also comes from the deletion of cross coupling terms between the neglected motions and remaining forces, the neglected forces and the remaining motions, and the neglected forces and the neglected motions;A number of numerical-experimental hybrid measurement methods are proposed and evaluated for finding the multidirectional driving point and transfer point accelerance matrices in both 2D and 3D. These methods are tested for their robustness under conditions of noisy data. A 2D implementation, called a T-bar, and a 3D implementation, called a C-bar, of an elastic test attachment structure, called "Instrument Cluster", are developed. Accelerometers are embedded in the "Instrument Cluster". The finite element model is an integral part of the experimental testing process. The FE FRF's of the "Instrument Cluster" are used together with the experimental FRF's of the combined structure. A new rotational accelerometer is used to obtain better rotational acceleration than two closely spaced linear accelerometers. Experimental results show this method is both feasible and promising.