Several catalytic reactions such as partial oxidations and hydrogenations are carried out in packed-bed reactors with diameter-to-length (aspect) ratios of order unity and a reactor-to-particle diameter ratios of 20 or more. In the design and operation of these reactors one objective is to prevent the side reactions that may occur due to localized hot spots or temperature variations. In such reactors, the transport coefficients in the flow and transverse directions can be quite different. In the present study, we report a new type of instability, the transverse instability, which leads to non-uniform temperature and concentration profiles in the lateral direction (across the diameter). This instability can occur even when the physical property variations are negligible and velocity is constant and unidirectional. We consider a reaction of the type A + nu B --> P with a Langmuir-Hinshelwood-type kinetic expression and use a pseudohomogeneous model. For a fixed number of catalyst particles in the direction of flow (L/d(p)), the boundary that determines the onset of transverse concentration and temperature nonuniformities is presented in the parameter space defined by the number of catalyst particles in the transverse direction (R/d(p)) and the residence time (Da). Our results indicate that transverse nonuniformities are likely to occur for typical values of the reaction parameters when the reactor to particle diameter exceeds about 5. For aspect ratios of order unity, this number is nearly independent of the number of particles in the flow direction.