This paper shows the state of the art of Mexican asphalt, AC-20 grade, modified by linear styrene-butadiene triblock copolymers (SBS), which include variations in their chemical structures, specifically, total styrene and 1,2-butadiene vinyl contents. The main objective of this work was studying the influence of variation in the 1,2-butadiene vinyl content between 9 to 41% (wt/wt), and also variation in the styrene content between 10 and 45% (wt/wt). Both variables were changed in the structure for the SBS copolymer in order to see the effect on thermal and rheological properties when they are used as asphalt modifiers. The research includes composition characterization and thermal properties of raw and modified asphalt. Analytical characterization of SBS polymers was carried out too by means of differential scanning calorimetry, fluorescence microscopy, and a parallel plate rheometer. Results obtained showed that SBSs with a molecular weight of 200000 +/-10000 Daltons get the maximum performance in the softening point and maximum rheological failure temperature when the styrene content is around 30% and vinyl groups move from 20 to 30% into the polymer microstructure with an appropriate viscosity level at 135 degrees C according to Strategic Highway Research Program standards.