Considering that there are undesired outputs in many production processes and the fact that the data for the efficiency evaluation contain random errors，a random DEA model was built for the above two prob_x005flems．The model defined the priority of the decision-making units through introducing the concept of risk and depicted the weak disposability of the undesired outputs by applying the " correlation" concept from statistics．This paper combined the randomness and the weak disposability in the framework of optimization theory to build the evaluation model that could investigate both．The empirical analysis investigated the similarities and differences of the model’s evaluation results under different levels of random errors and under the consideration of weak disposability or not．The results showed that the model can solve the problem of undesirable outputs and random errors in the data．In conclusion，the model，with broad applicability，is superior to the existing models．