We describe in this article the techniques developed for the robust treatment of the static energy versus volume theoretical curve in the new version of the quasi-harmonic model code Comput. Phys. Commun. 158 (2004) 57. An average of strain polynomials is used to determine, as precisely as the input data allow it, the equilibrium properties and the derivatives of the static E(V) curve. The method provides a conservative estimation of the error bars associated to the fitting procedure. We have also developed the techniques required for detecting, and eventually removing, problematic data points and jumps in the E(V) curve. The fitting routines are offered as an independent octave package, called AsturFit, with an open source license. Program title:AsturFit Catalogue identifier: AEIY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIY_v1_0.html Program obtainable from: CPC Program Library, Queenʼs University, Belfast, N. Ireland Licensing provisions: GPL version 3 No. of lines in distributed program, including test data, etc.: 21 347 No. of bytes in distributed program, including test data, etc.: 620 496 Distribution format: tar.gz Programming language: GNU Octave Computer: Workstations Operating system: Unix, GNU/Linux Classification: 4.9 External routines: The GSL and OPTIM packages from the octaveforge site (http://octave.sourceforge.net/). Nature of problem: Fit the total energy versus volume data of a solid to a continuous function and extract the equilibrium properties and the derivatives of the energy, with an estimation of the error introduced by the fitting procedure. Solution method: The use of averages of strain polynomials allows a robust and reliable representation of the energy curve and its derivatives, together with a statistical estimation of the goodness of the calculated properties. Additional comments: The techniques discussed have been implemented in Gibbs2, to be included with the second part of this article. Included here is the OCTAVE implementation of the routines, useful for interactive work and also for the creation of independent scripts. Some representative examples are included as test cases with a collection of data sets, test scripts, and model outputs. Running time: Seconds at most in routine uses of the program. Special tasks like the bootstrap analysis may take up to some minutes. ► Robust fitting of energy versus volume curves using averages of strain polynomials. ► Error bars associated to the fits and thermodynamic properties. ► Detection of noise and problems in the input data. ► An octave package implementing the technique: Asturfit.