Hanshik(cold meal) day is one of the four big festival days in the Oriental tradition along with the New Year's day, Danoh day and Chusok day. Hanshik is not fixed as is Easter Sunday, whereas the others are fixed; the New Year's day, the 1st of January, Danoh, the 5th of May, and Chusok, the 15th of August by the lunar calendar. This is a study on the periodicity of Hanshik when it overlaps with Chongmyong(Clear and Bright) day. It is found that generally Hanshik has periodicities of 4 years, 29 years, 33 years and 128 years, which are the basic plan of leap years. It also includes 103 year period which is that of the sexagenary cycle of days of the 24 solar terms.