An accurate synthesis model applied to multilayer probe-fed microstrip antennas, is presented. An appropriate and original use of a symbolic algebra system and a modified Wolff cavity model allow to obtain, with a low computing time, the optimal size and the shape of the antenna, with its uncertainty, versus the physical and geometrical parameters, necessary to a good approach. The numerical and experimental results for different synthesis are shown and discussed.INTgDC;ILONT hese last years, a great number of models have aimed at determining the electrical characteristics of printed antennas of various shapes with a good agreement with experiments and other rigorous investigations. However, at our knowledge, a synthesis model for multilayer probe-fed microstrip antennas with or without an air-gap, taking into account the shape of the element has not been yet published. We show in figure 1 and figure 2-the different studied structures. An air-gap enables to obtain exactly the resonant impressed frequency (1-2), the dielectric cover can offer protection against environmental hazards (ice, snow for example) (3-6), the ring microstrip antenna can be proposed for dual band operation (7-9), and the eccentricity of the elliptical antenna allows us to obtain a wider frequency band and the desired resonant frequency (10-12).For all these reasons, we propose an original synthesis model whose the calculation of uncertainties is obtained by a symbolic algebra system (Maple V.2). The analytical model introduced in the synthesis, takes into account aWof this parameters and tl a ntages and drawback of each shape and proposed the best structuiv`p0,sible for each case. Sfrcwical criteria like bandwidth, quality of polarisation, circular polarisation or efficiency versus the shape of the element are associated concurrently with geometrical and physical parameters. s -Protecive layer ==~~~~~&c.tg&, Hc a Radiating element Dielectric Substi -t /rs,tg8s,H s Air-gap