Since the appearance of digital audio recordings, audio authentication has been becoming increasingly difficult. The currently available technologies and free editing software allow a forger to cut or paste any single word without audible artifacts. Nowadays, the only method referring to digital audio files commonly approved by forensic experts is the ENF criterion. It consists in fluctuation analysis of the mains frequency induced in electronic circuits of recording devices. Therefore, its effectiveness is strictly dependent on the presence of mains signal in the recording, which is a rare occurrence. Recently, much attention has been paid to authenticity analysis of compressed multimedia files and several solutions were proposed for detection of double compression in both digital video and digital audio. This paper addresses the problem of tampering detection in compressed audio files and discusses new methods that can be used for authenticity analysis of digital recordings. Presented approaches consist in evaluation of statistical features extracted from the MDCT coefficients as well as other parameters that may be obtained from compressed audio files. Calculated feature vectors are used for training selected machine learning algorithms. The detection of multiple compression covers up tampering activities as well as identification of traces of montage in digital audio recordings. To enhance the methods' robustness an encoder identification algorithm was developed and applied based on analysis of inherent parameters of compression. The effectiveness of tampering detection algorithms is tested on a predefined large music database consisting of nearly one million of compressed audio files. The influence of compression algorithms' parameters on the classification performance is discussed, based on the results of the current study.