Abstract: A model of an expanded universal Turing machine（EUTM） based on the model of Turing machine is proposed,which is the basic theory of computer, and the infection of computer viruses is formally described according to the EUTM model in the circumstance of a single machine and multi machine environment The procedure or virus is considered as the code of Turing machine, and the code of Turing machine is regarded as the input of the EUTM model EUTM reads the inputs,copies the inputs on the storage’s tape, and at the same time writes the results on the output’s tape A procedure is a virus iff ① ‖Φ v（p）‖ =‖v‖‖x‖;② 〈Φ v（p）〉〈v〉 or 〈Φ v（p）〉〈V（v）〉;③ Φ v（p） has the properties of procedure v , that is to say, Φ Φ（p′） satisfies the condition 1 and 2 The deficiencies of Fred Cohen’s proof about virus undetectability theory are pointed out And the theory of virus undetectability is proved based on the EUTM model The model of the EUTM simplifies the formal description of computer viruses’ infection and emphasizes the basic property of computer viruses