Cortical spreading depression (CSD) is a slowly propagating wave of depolarization of brain cells, followed by temporary silenced electrical brain activity. Major structural changes during CSD are linked to neuronal and possibly glial swelling. However, basic questions still remain unanswered. In particular, there are open questions regarding whether neurons or glial cells swell more, and how the cellular swelling affects the CSD wave propagation.In this study, we computationally explore how different parameters affect the swelling of neurons and astrocytes (starshaped glial cells) during CSD and how the cell swelling alters the CSD wave spatial distribution. We apply a homogenized mathematical model that describes electrodiffusion in the intraand extracellular space, and discretize the equations using a finite element method. The simulations are run with a twocompartment (extracellular space and neurons) and a threecompartment version of the model with astrocytes added. We consider cell swelling during CSD in four scenarios: (A) incorporating aquaporin-4 channels in the astrocytic membrane, (B) increasing the neuron/astrocyte ratio to 2:1, (C) blocking and increasing the Na/K-ATPase rate in the astrocytic compartment, and (D) blocking the Cl channels in astrocytes. Our results show that increasing the water permeability in the astrocytes results in a higher astrocytic swelling and a lower neuronal swelling than in the default case. Further, elevated neuronal density increases the swelling in both neurons and astrocytes. Blocking the Na/K-ATPase in the astrocytes leads to an increased wave width and swelling in both compartments, which instead decreases when the pump rate is raised. Blocking the Cl channels in the astrocytes results in neuronal swelling, and a shrinkage in the astrocytes. Our results suggest a supporting role of astrocytes in preventing cellular swelling and CSD, as well as highlighting how dysfunctions in astrocytes might elicit CSD.