Residual stresses are common in Micro Electro Mechanical System (MEMS) membrane structures. Experimental assessment of these stresses can provide valuable information on the production process. In general, experimental stress assessment for MEMS is challenging due to the limited possibilities for non-destructive testing. This work investigates the use of dynamic modal data to identify the residual stress state. In view of the computational feasibility, the focus is on two aspects: 1) A method is proposed that expresses the unknown stress field as a combination of few, carefully selected stress modes. An optimization algorithm is deemed to identify the amplitudes of such modes. 2) A meta-model is constructed using the empirical interpolation method (EIM), to facilitate a fast evaluation of the iterations.