The basal ganglia are important for action initiation, selection, and motor learning. The input level, the striatum, receives input preferentially from the cortex and thalamus and is to 95% composed of striatal projection neurons (SPNs) with sparse GABAergic collaterals targeting distal dendrites of neighboring SPNs, in a distance-dependent manner. The remaining 5% are GABAergic and cholinergic interneurons. Our aim here is to investigate the role of surround inhibition for the intrinsic function of the striatum. Large-scale striatal networks of 20 to 40 thousand neurons were simulated with detailed multicompartmental models of different cell types, corresponding to the size of a module of the dorsolateral striatum, like the forelimb area (mouse). The effect of surround inhibition on dendritic computation and network activity was investigated, while groups of SPNs were activated. The SPN-induced surround inhibition in distal dendrites shunted effectively the corticostriatal EPSPs. The size of dendritic plateau-like potentials within the specific dendritic segment was both reduced and enhanced by inhibition, due to the hyperpolarized membrane potential of SPNs and the reversal-potential of GABA. On a population level, the competition between two subpopulations of SPNs was found to depend on the distance between the two units, the size of each unit, the activity level in each subgroup and the dopaminergic modulation of the dSPNs and iSPNs. The SPNs provided the dominating source of inhibition within the striatum, while the fast-spiking interneuron mainly had an initial effect due to short-term synaptic plasticity as shown in with ablation of the synaptic interaction.