Patient-derived xenografts (PDXs) are resected human tumors engrafted into mice for preclinical studies and therapeutic testing. It has been proposed that the mouse host affects tumor evolution during PDX engraftment and propagation, affecting the accuracy of PDX modeling of human cancer. Here, we exhaustively analyze copy number alterations (CNAs) in 1,451 PDX and matched patient tumor (PT) samples from 509 PDX models. CNA inferences based on DNA sequencing and microarray data displayed substantially higher resolution and dynamic range than gene expression-based inferences, and they also showed strong CNA conservation from PTs through late-passage PDXs. CNA recurrence analysis of 130 colorectal and breast PT/PDX-early/PDX-late trios confirmed high-resolution CNA retention. We observed no significant enrichment of cancer-related genes in PDX-specific CNAs across models. Moreover, CNA differences between patient and PDX tumors were comparable to variations in multiregion samples within patients. Our study demonstrates the lack of systematic copy number evolution driven by the PDX mouse host.