It is well known that the presence of large heterogeneous textured regions in forged near alpha titanium alloys could lead to large variations of mechanical properties when fatigue and creep cycles are applied at room temperature. On the other hand, experimental studies and microtexture investigations are complex to set up, lengthy and costly, and one cannot expect to understand the alloy behavior by relying only on empirical approaches. Hence, numerical methods are excellent alternatives for analyzing the influence of microscopic and macroscopic heterogeneities on mechanical properties in shorter times and with minimum need for experimentation. In the present investigation, a cellular automata (CA) method was used to simulate the effect of texture heterogeneities, on both local and global mechanical properties. A 2D array of cells was used and the stresses and strains developed in various heterogeneous regions were evaluated using the Eshelby theory. Using the CA method, various types of microstructures were modeled and compared with each other to quantify the influence of processing parameters on mechanical properties. The results predict, and are used to explain, the experimentally phenomena observed in creep responses during cold fatigue/creep tests of near alpha titanium samples