This paper investigated English modal auxiliary verbs can and may in three East Asian EFL learners' writings (Chinese, Japanese, and Korean). For the investigation, two different types of corpora were adopted. One is the ICE-USA corpus which included the writings of the English as a Native Language (ENL) speakers and the TOEFL11 corpus which contained the writings of the English as a Foreign Language (EFL) learners. Among the eleven sections of the TOEFL11 corpus, three components were selected in the analysis. This paper was theoretically based on Bates and MacWhinney's Competition Model (1982, 1989), and four language models were statistically constructed. These models were constructed as follows. From the four different corpora, all the sentences with can and may were extracted, and twenty linguistic factors were manually encoded. Then, the statistical models were constructed based on the encoded corpus data, and similarities and differences were analyzed in the statistical models. Two different types of statistical analyses were adopted. One was a logistic regression, and the other was a Behavioural Profiles analysis. Through the analysis, the following facts were observed: (i) six linguistic factors were involved in the choice of alternation, (ii) eight linguistic factors were interact with L1 which made three East Asian EFL learners' writings non-native, and (iii) the uses of can and may by the three East Asian EFL learners were different from those of the ENL speakers.