Singular stress analysis in the flat punch problem of half-plane is carried out. The angle distribution for the stress components is also achieved in an explicit form. Followed a similar study in the punch analysis, the punch singular stress factor (abbreviated as PSSF) is defined from the singular stress distribution. For the problems of two punches or three punches, solutions in a closed form are obtained. The obtained solutions may depend on some complete elliptical integrals. Meantime, the exerting location of the resultant force for punches is also determined. Interactions between punches are also addressed. Several numerical examples with the calculated results are presented.