A system of propagating cracks may explain magma transport and the evolution of a volcano. This paper considers only a basaltic magma. The system is controlled by two boundary conditions: the stress field, and the production rate of the magma-filled cracks in the mantle. Numerical solutions of crack propagation for various stress conditions, with a constant production rate high enough to coalesce isolated cracks, were performed, and the results applied to different tectonic conditions. For the hydrostatic stress conditions, most magma-filled cracks beneath a polygenetic volcano become trapped either in the lower crust, because there the density difference between magma and the host rocks (Δρ) becomes suddenly small, compared with that in the mantle, or trapped in the upper crust, because there Δρ is near to zero. Magma traps composed of such cracks may grow into magma reservoirs if the production rate of cracks in the mantle is large. If horizontal stress with a vertical gradient is superimposed on the hydrostatic condition in the crust, that is, tensile stress which increases upward or compressional stress which increases downward, magmafilled cracks, even if the density of magma is higher than that of the crust, may ascend directly without trapping. When the crust undergoes relative tension, magma-filled cracks may become trapped. Then, the lower part of the trap may grow into a magma reservoir, while the upper part may become filled with dikes. When the production rate of cracks is small, an initial magma-filled crack can rise directly to the surface only when the stress with a gradient is superimposed as mentioned above, or when the average density in a crack decreases, owing to, for example, vesiculation of volatile components.