Nowadays, many optical elements are fabricated by means of glass molding using hard and brittle inserts such as Silicon Carbide (SiC) and Silicon Nitride (Si3N4). However, for those hard-to-machine materials, the most feasible solution is still with ultra-precision grinding and following polishing. Hence, it is necessary and meaningful to study their plastic properties for the development of optical fabrication and ultra-precision manufacturing process. However, the conventional methods including compression test and indentation fracture mechanics are not sufficient to obtain the accurate parameters and still lack of reliable supporting of the machining process. To solve this problem, this paper presents a novel way to correlate the plastic properties to the indentation data using dimensional analysis for the two sorts of hard and brittle materials of SiC and Si3N4. Through integrating the data obtained by the indentation tests and the modeling method presented in this paper, stress-strain behavior, yield stress σy, yield strain epsilony and strain hardening exponent n could be determined. The processing performance of these two materials reflected by the above parameters are consistent with the conclusions drawing from the indentation crack development under varying loads during the indentation test, which verifies the effectiveness and feasibility of the presented modeling method.