Planning, a prospective form of short-term memory, is a cognitive function that has been predominantly attributed to the cortex. Recent experiments, however, have concluded that the thalamus and other subcortical structures participate in this function. A comprehensive computational framework to link neural dynamics and cognition in the context of large-scale subcortical-cortical circuits is lacking. In this computational study, we elucidated the dynamical mechanisms by which the cortex, thalamus and other subcortical structures jointly contribute to planning. Recurrent circuitry in the cortex generates stimulus-selective activity patterns, which are maintained by reciprocal corticothalamic projections across a memory epoch. Subcortical signals are routed through the thalamus to selectively modify these patterns, for example enabling execution after planning. We refer to this dynamical process as subcortex control of activity modes, as the cortical activity patterns (‘activity modes’) are low-dimensional in comparison to the number of neurons that are modulated by the task. We evaluated the implications of subcortex control by simulating networks of interconnected thalamic and cortical ‘rate’ units in the context of a motor planning task. In tight link with electrophysiological data from mice, we identified subcortical excitatory and inhibitory contributions to the planning computations during the memory epoch. Our model predicts that the distinct computational roles of the pars reticulata (SNr) and thalamic reticular nucleus (TRN) during planning (Wang et al., 2021) are a result of their specific selectivity-dependent connectivity patterns with the thalamus. Moreover, the ‘switch’ from movement planning to execution (Inagaki et al., 2021) is instantiated by a midbrain-mediated thalamic burst, which uncovers a latent motor instruction that is stored in deep cortical layers during the memory epoch. Overall, we propose a novel framework to analyze planning computations in terms of cortical activity modes, which are shaped by subcortical structures via the thalamus based on task demands.