Explaining the decisions made by a radiomic model is of significant interest, as it can provide valuable insights into the information learned by complex models and foster trust in well-performing ones, thereby facilitating their clinical adoption. Promising radiomic approaches that aggregate information from multiple regions within an image currently lack suitable explanation tools that could identify the regions that most significantly influence their decisions. Here we present a model- and modality-agnostic tool (RadShap, https://github.com/ncaptier/radshap), based on Shapley values, that explains the predictions of multiregion radiomic models by highlighting the contribution of each individual region. Methods: The explanation tool leverages Shapley values to distribute the aggregative radiomic model's output among all the regions of interest of an image, highlighting their individual contribution. RadShap was validated using a retrospective cohort of 130 patients with advanced non-small cell lung cancer undergoing first-line immunotherapy. Their baseline PET scans were used to build 1,000 synthetic tasks to evaluate the degree of alignment between the tool's explanations and our data generation process. RadShap's potential was then illustrated through 2 real case studies by aggregating information from all segmented tumors: the prediction of the progression-free survival of the non-small cell lung cancer patients and the classification of the histologic tumor subtype. Results: RadShap demonstrated strong alignment with the ground truth, with a median frequency of 94% for consistently explained predictions in the synthetic tasks. In both real-case studies, the aggregative models yielded superior performance to the single-lesion models (average [±SD] time-dependent area under the receiver operating characteristic curve was 0.66 ± 0.02 for the aggregative survival model vs. 0.55 ± 0.04 for the primary tumor survival model). The tool's explanations provided relevant insights into the behavior of the aggregative models, highlighting that for the classification of the histologic subtype, the aggregative model used information beyond the biopsy site to correctly classify patients who were initially misclassified by a model focusing only on the biopsied tumor. Conclusion: RadShap aligned with ground truth explanations and provided valuable insights into radiomic models' behaviors. It is implemented as a user-friendly Python package with documentation and tutorials, facilitating its smooth integration into radiomic pipelines.