Intracerebral hemorrhages (ICHs) occur in 24 out of 100,000 people annually and have high morbidity and mortality rates. The standard treatment is conservative. We hypothesize that a patient-specific, mechanical model coupled with a robotic steerable needle, used to aspirate a hematoma, would result in a minimally invasive approach to ICH management that will improve outcomes. As a preliminary study, three realizations of a tissue aspiration framework are explored within the context of a biphasic finite element model based on Biot's consolidation theory. Short-term transient effects were neglected in favor of steady state formulation. The Galerkin Method of Weighted Residuals was used to solve coupled partial differential equations using linear basis functions, and assumptions of plane strain and homogeneous isotropic properties. All aspiration models began with the application of aspiration pressure sink(s), calculated pressures and displacements, and the use of von Mises stresses within a tissue failure criterion. With respect to aspiration strategies, one model employs an element-deletion strategy followed by aspiration redeployment on the remaining grid, while the other approaches use principles of superposition on a fixed grid. While the element-deletion approach had some intuitive appeal, without incorporating a dynamic grid strategy, it evolved into a less realistic result. The superposition strategy overcame this, but would require empirical investigations to determine the optimum distribution of aspiration sinks to match material removal. While each modeling framework demonstrated some promise, the superposition method's ease of computation, ability to incorporate the surgical plan, and better similarity to existing empirical observational data, makes it favorable.