This paper formally incorporates allele measurement error into the Essen-Möller version of the probability of paternity. For highly polymorphic genetic systems, an approximate solution to the problem is developed resulting in simple formulas. The DNA sequence of the D14S1 region provided a practical example for testing this approximation. For these sequences, allelic uncertainty arises from determining length of DNA fragments from mobility in gel electrophoresis. D14S1 and standard test results from 35 paternity cases establish the validity of our computational method.