In this paper, we present a method to fabricate long period gratings in standard telecommunications single mode fibers (SSMF), using a femtosecond laser system. A numerical model based on the coupled mode theory was developed and implemented with the aim to guide and improve the inscribing technique. This model takes in consideration the specifications of the inscription technique. Using this model, we have analyzed the behavior of the gratings for different irradiation lengths per period, refractive index modulation values and considering first and second order coupling with different cladding modes. LPGs inscribed in SSMF are presented, its transmission spectra were analyzed and a good agreement between the numerical results and the experimental LPGs was achieved. The sensitivity to temperature of the produced LPGs was also characterized, attaining different sensitivities for different attenuation peaks.