Wire antenna models are a useful approach for studying small cylindrical elements using Integral Equation (IE) formulations [1, 2, 3]. For an accurate application of these models in the Method of Moments (MoM), some techniques must be derived in order to properly deal with the singularity of the kernel term, which is related to the behavior of the elliptic integral functions. In previous works exact expressions are obtained for the integration of the kernel along wire cells, but as a major drawback they are expressed in terms of infinite summations, which are slowly convergent near the singular condition of the observation point. In this work, an alternative technique is proposed, using a decomposition of the singular elliptic function in terms of a polynomial expansion [4]. This method isolates the real singular term of the elliptic integral in a simple expression that can be performed analytically. The rest of the derived terms are regular, and numerical integration can be employed. Using this semianalytical approach, the different integrals involved in the evaluation of the electromagnetic fields can be evaluated with higher accuracy, as it will be shown in the communication.