Unconventional plays such as Vaca Muerta are geologically complex and heterogeneous. Wells must be hydraulically fractured to produce, and material fabric, material properties, and in situ stress strongly influence this process. When logs are not available in the laterals, measurements on drill cuttings can be used to estimate anisotropic mechanical properties and stresses. The proposed method relies on two main steps. First, using one or more data-rich pilot wells, we define and calibrate rock physics and geomechanical models. The rock physics model provides the necessary relationship between the petrophysical volumes (mineralogy, organic matter and fluids) and the elasticity moduli, and the geomechanics model the relationship between elasticity moduli and the stress indices and the minimum stress. Second, in nearby lateral wells, we measure mineralogy and organic matter on cuttings samples using Diffuse Reflectance Infrared Fourier Transform Spectroscopy (DRIFTS) and apply the models to compute the elastic and stress properties. We illustrate this method using two vertical pilot wells that cross the Quintuco and Vaca Muerta Formations, Argentina, and one horizontal lateral well in Vaca Muerta. A complete suite of petrophysics logs have been acquired in both pilots, in addition to DRIFTS measurements on cutting samples in one of them and rock mechanics lab measurements on cores in the other one. In the lateral well, DRIFTS data have been acquired. We limit this paper to the construction, calibration and application of the rock physics model, as the construction and calibration of the geomechanical model is reported in a companion paper. We show that the sonic moduli can be reconstructed very accurately from the petrophysical volumes in the Quintuco and Vaca Muerta formations. The rock physics model highlights the impact of the high TOC in Vaca Muerta and of the mineralogy in Quintuco. The anisotropic shear moduli of Vaca Muerta are also predicted satisfactorily. To demonstrate the methodology, DRIFTS measurements on cuttings from the pilot well, are used to predict the sonic-derived moduli. Despite the sampling of the cuttings every few meters compared to the log data every 15 cm, we show an excellent consistency between DRIFTS- and log-derived elastic moduli. The model is then applied to DRIFTS data acquired on cuttings in a lateral, and the cutting-derived stress indices are computed. This method is both practical and theoretically sound. First, deterministic rock physics and geomechanics models are calibrated with high-resolution log data in a pilot well to relate petrophysical volumes to stress properties. Second, the use of spectroscopy logs in pilots and spectroscopy measurements on cuttings in laterals allow accurate estimation of stresses using cutting-based measurements in data-lean environments.