A resonant planar antenna as an inductive plasma source operating at 13.56 MHz inside a low pressure vacuum vessel is presented for potential plasma processing applications. Its principle consists in interconnecting elementary resonant meshes composed of inductive and capacitive elements. Due to its structure, the antenna shows a set of resonant modes associated with peaks of the real input impedance. Each of these modes is defined by its own current and voltage distribution oscillating at the frequency of the mode. A rectangular antenna of 0.55 m x 0.20 m has been built, and first results obtained with argon plasmas are presented. Plasma generation is shown to be efficient as densities up to 4 x 10(17) m(-3) at 2000 W have been measured by microwave interferometry at a distance of 4 cm from the source plane. It is also demonstrated that the plasma couples inductively with the resonating currents flowing in the antenna above a threshold power of about 60 W. A non-uniformity of less than +/- 5% is obtained at 1000 W at a few centimeters above the antenna over 75% of its surface. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4705978]