Down syndrome (DS) is a genetic disorder occurring in 1 out of every 700 to 1,000 live births caused by trisomy of chromosome 21. The overexpression of the Amyloid Precursor Protein (APP) gene located on this chromosome leads to an early onset and rapid accumulation of ß‐amyloid (Aß) in the brain that invariably results in Alzheimer Disease (AD) in people with DS. Therefore, AD, the most common form of dementia, is currently one of the most relevant medical issues in people with DS. In this study, we assessed brain morphological patterns to quantify dysmorphologies associated with AD in Down syndrome. Brain shape and size analyses were performed using Geometric Morphometrics in a sample of 243 adults, including 153 euploid healthy controls (EU) and 90 individuals with DS at different stages of dementia: asymptomatic DS with no signs of AD‐related cognitive impairment (N=58), individuals with DS and prodromal AD (N=21) and individuals diagnosed with AD dementia (N=11). A set of 38 3D brain landmarks representing the overall shape of the brain and internal brain structures (ventricles, corpus callosum, cerebellum and pons) were located on magnetic resonance images of the head. Results showed a significant separation between EU and DS populations based on both global and local brain shape and size analyses. Individuals with DS displayed a smaller cerebellum, a protruding posterior midbody in the corpus callosum, a frontally projected brain and expanded ventricles. Significant brain shape differences were detected in individuals diagnosed with AD, which mainly affected the shape of enlarged brain ventricles. Remarkably, individuals at advanced stages of the disease displayed more severe dysmorphologies as compared to those individuals at prodromal stages and individuals with no signs of dementia, confirming a phenotypic continuum associated with the severity of dementia that highlights the impact of this neurodegenerative disorder in brain morphology.