The standard mathematical procedures in Helioseismology field are based on normal mode approach for various models of solar interior and atmosphere. We consider a two region model of a system solar interior and solar atmosphere. For simplicity, the two different regions are assumed quasi-isothermal, semi-infinite, without magnetic fields and separated by a boundary z=0. It was found useful to phrase of stability as initial value problem (IPV) in order to ensure the inclusion of certain

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... modes otherwise neglected. In addition to discrete mode (f-mode), sets of continuum modes due to a branch cuts in the complex plane, not treated explicitly in the literature, appears. It will be seen that an ambiguity of the usual normal mode method is avoided.