Silos are a type of unconventional structure widely used by industries and agro farms for storage of all types of grains. Because of the complexity of the seismic behavior of silo-grain systems, it is not trivial to evaluate the seismic responses quickly and reliably. This paper presents mathematical expressions to evaluate the following responses of interest in a circular reinforced concrete silo: the fundamental period of vibration, lateral displacements, shear forces and overturning moments. These expressions are based on a linear elastic model that can represent the structural behavior of silo-grain system, and the design spectrum of Peruvian standard E030 was considered as seismic action. The most relevant geometric and physical parameters that govern the behavior of silo-grain system were identified, and it was considered that the grain has a soil-like behavior. The linear elastic model of the silo is given by a spring-mass system, with a number of discretized elements representing its structure. With the model, differential equation of motion were formulated and were solved using spectral modal combination method, finding the responses of interest mentioned above. These results were compared with those obtained using a refined finite element model to validate the proposed model. A margin of error between 15% and 20% was achieved, which is acceptable in civil engineering. Finally, the simplified methods for calculating the response of interest were obtained from the validated response.