By proving the existence of the minimum of the threshold function in (0; 1) we show that the threshold of regular lowdensity erasure codes under erasure recovery algorithms is equal to the minimum of the threshold function in (0; 1). The existence and uniqueness of positive real root of the polynomial equation k(x) = 0 in [0; 1) are verified. It follows from the two conclusions obtained above that the threshold of regular low-density erasure codes can be determined by the analytical expression.