Stomach cancer belongs to the most common malignant tumors in Portugal. Main causal factors are age, dietary habits, smoking, and Helicobacter pylori infections. As these factors do not only operate on different time dimensions, such as age, period, or birth cohort, but may also vary along space, it is of utmost interest to model temporal and spatial trends jointly. In this paper, we analyze incidence of stomach cancer in Southern Portugal between 1998 and 2006 for females and males jointly using a spatial multivariate age-period-cohort model. Thus, we avoid age aggregation and allow the exploration of heterogeneous time trends between males and females across age, period, birth cohort, and space. Model estimation is performed within a Bayesian setting assuming (gender specific) smoothing priors. Our results show that the posterior expected rate of stomach cancer is decreasing for all counties in Southern Portugal and that males around 70 have a two times higher risk of getting stomach cancer compared with their female counterparts. We further found that, except for some few counties, the spatial influence is almost constant over time and negligible in the southern counties of Southern Portugal.