Abstract: As a main purpose,the transfer of errors by the Theis equation itself under the situation that the input data has the random errors and utilizing the Theis equation to the direct and inverse computation problems,i.e.,the performance of Theis equation,is analyzed.Applying the randomness analysis method of the data random errors transfer by the functions and the simpler mathematical derivation,the approximate expressions between the statistic parameters of the random errors of input and output data have been established,and the conditional function for both kinds of computation problem are derived.It is indicated that in the case of smaller value of u,the condition for computing u is bad performance;in the case of u=0.438 and nearby,that for computing T is bad performance;and in the case of larger u value and large ratio of relative errors of _and T,the direct computation problem is bad performance too.The computation problems under other conditions belong to good performance.On this basis,it is recommended that the calculation of T value utilizes the data from later stage of pumping test,and that of the_value utilizes the data from early stage.In addition,the errors estimation method is presented if the errors of original data is known.