Electromagnetic fields behavior is determined by Maxwell equations and boundary conditions. Therefore, the electromagnetic field can be regulated by choosing the proper boundary conditions. The most common boundary condition is perfect electric conductor PEC which can be realized by good conductive materials in microwave frequency range. The other useful boundary condition is perfect magnetic conductor (PMC). Although there is no natural magnetic conductor, there are artificial magnetic conductors (AMC) which exhibit PMC-like behavior at certain frequencies. Artificial magnetic conductors are realized using periodic planar structures. These surfaces can also be engineered to suppress surface waves. They have been applied in miniaturized antennas for improving the input impedance matching, enhancing the radiation pattern, reducing the back lobes and increasing the antenna gain. They are also exploited in realizing TEM-wave guides and radar cross section reduction coatings. Unfortunately PMC-like behavior of artificial magnetic conductors occurs in a limited frequency range (AMC bandwidth). Extensive amount of research has been done to increase the bandwidth. It is also desirable for an artificial magnetic conductor to suppress surface waves at its PMC-like behavior band. Therefore, it has been tried to establish the relation between the in-phase reflection band and the surface wave suppression band ( surface wave band-gap) of the artificial magnetic conductors. In the thesis fundamental properties of in-phase reflection of artificial magnetic conductors are demonstrated and an upper limit for in-phase reflection bandwidth is proposed. The upper limit of bandwidth is validated for different structures. The simulation results show that the proposed limit can properly predict the maximum achievable bandwidth. The qualitative effects of artificial magnetic conductor structural parameters on its operating frequency are investigated for a general case. To determine the relation between reflection phase and surface wave band-gap , artificial magnetic conductor surface is modeled by equivalent surface impedance. Using the dispersion equation and reflection coefficient associated with this surface impedance, the relation between the reflection phase and the surface wave band-gap is shown and a procedure is proposed for finding the dispersion equation from the reflection data. Keywords: Artificial magnetic conductor, electromagnetic band-gap, in-phase reflection, surface wave suppression