In the process of cell division, chromosomes are segregated by mitotic spindles—bipolar microtubule arrays that have a characteristic fusiform shape. Mitotic spindle function is based on motor-generated forces of hundreds of piconewtons. These forces have to deform the spindle, yet the role of microtubule elastic deformations in the spindle remains unclear. Here we solve equations of elasticity theory for spindle microtubules, compare the solutions with shapes of early Drosophila embryo spindles and discuss the biophysical and cell biological implications of this analysis. The model suggests that microtubule bundles in the spindle behave like effective compressed springs with stiffness of the order of tens of piconewtons per micron, that microtubule elasticity limits the motors' power, and that clamping and cross-linking of microtubules are needed to transduce the motors' forces in the spindle. Some data are hard to reconcile with the model predictions, suggesting that cytoskeletal structures laterally reinforce the spindle and/or that rapid microtubule turnover relieves the elastic stresses.