Drilling, followed or interrupted sometimes by interventions or overhauling activities, is one of the most costly and full of the possibility of danger or failure activity. Failure of one of rig components, and in particular the mast, can lead to very big and unwanted cost implications. The question of masts vibrations is a concern for drillers and, also, for design engineers during the rigs functioning in oil fields. It is obvious that, for a given construction of a mast, is necessary to know in advance its natural frequencies values, in order to avoid them during rig’s work. In this paper it is analyzed the dynamic behaviour of a transportable mast of 500 kN maximum hook load, in the case of the free vibrations. The mast is made out of three sections: a fix, an inferior and a superior section, composing a complex spatial structure, statically undetermined. In its assembly, the mast is made out of straight beams with different cross-sections, being linked to truck chassis by the means of four strength anchors: two, fixed at the crown block’s level and two at the top of the inferior part. Authors used the Finite Elements Analysis with the aim to determine the first ten natural frequencies and the correspondent mode shapes for the first five. The evaluation of all factors which can produce forced vibrations during rig’s functioning and the risks of the appearance of resonance phenomenon are pointed out.