This paper reports on the results of numerical investigations of the influence of an external feedback on the longitudinal modes of a semiconductor laser. The numerical calculations are based on the solution of the homogeneous coupled-mode equations using a transfer function approach. We study the three section external cavity diode laser shown in Fig. 1. It consists of an active section with length L₁, an air gap section with length L₂ and a passive Bragg grating section with length L₃. We show that the number of laser modes is strongly dependent on the transmission and reflection coefficients at the boundaries between the sections.  The basic parameters underlying the simulations are the following: wavelength , intensity reflectivity and transmission coefficients at the interface between active and gap sections equal 0.01 and 0.8, respectively, intensity reflectivity and transmission coefficients at the interface between gap and Bragg grating sections equal 0 and 1, respectively, L₁ = 1mm, L₂ = 30mm, L₃ = 6mm. The effective refractive index in the active section is set proportional to the injection current modelling the self-heating effect. As result of the simulation we obtain the lasing wavelengths or frequencies as a function of the injected current presented in Fig. 2. The decrease of the frequency with increasing current is caused by the increase of the effective index. If the detuning between the frequency of the mode and the constant Bragg frequency is too large, the lasing mode jumps back to a longitudinal mode having a higher frequency. Due to the fact that there are two (active + air gap) existing cavities, a further mode jump to a third mode and back occurs. Varying the transmission and reflection coefficients it is possible to change the number of participating modes. For example, if we reduce the reflection coefficient twice from original and set it equal to 0.005, keeping constant the value 0.8 of the transmission coefficient, only two modes are involved in the jumps. On the other hand, when we increase the reflection coefficient for a constant transmission coefficient, then the laser behavior become more complex and more modes are involved. A similar effect can be observed if we keep the reflection coefficient constant, but vary the transmission coefficient.