Abstract: An embodiment of the present invention provides portable magnetic toy construction system having a base plate upon which to build magnetic toy constructions, the base plate configured to accept and hold in position ferromagnetic or magnetic base elements, such as ferromagnetic balls. The base plate comprises at least one flexible membrane that stretches around a base element and holds the base element in position. The membrane exerts a force that holds the base element in position resisting lateral movement, although the elasticity of the flexible membrane still allows a user to manipulate the base element through the membrane to move the base element laterally. In one configuration, the base plate forms part of a travel case that can additionally include compartments to store magnetic building components. Further embodiments provide a magnetic toy construction, and a method for building the construction, that incorporate the base plate.