The Small Punch Test (SPT) has been widely used for the high throughput evaluation of mechanical properties of metallic materials. However, all the correlations between characteristic punch loads and mechanical properties measured from tensile tests thus far have been developed based on the variation of specimen thickness. This paper introduce a new approach to the estimation of tensile yield stress from punch test measured load-displacement curves based on the variation of punch indenter diameter. Mechanical properties of high density polyethylene (HDPE) are first characterized using both monotonic tensile and punch tests at various loading speeds. Linear correlations between the maximum punch load and the square indenter diameter or the indenter diameter are established, based on which the tensile yield stress could be expressed as a function of maximum punch load and the square indenter diameter or indenter diameter. The yield stress estimated using the proposed correlations is compared with those measured from tensile tests and the results indicate that the correlation based on the variation of indenter diameter yields better prediction results than the correlation based on the variation of square indenter diameter. Good agreement has been achieved between the predicted results using correlation based on the variation of indenter diameter and the yield stress measured from tensile tests, suggesting the proposed approach is applicable for the estimation of mechanical properties for HDPE materials based on punch test.