A method of mounting cars on a free standing space elevator tower. The actively stabilized space elevator tower has a segmented elevator core structure, each segment being formed of at least one pneumatically pressurized cell. The method of mounting the elevator cars allows the cars to ascend or descend on the outer surface of the elevator core structure or in a shaft on the interior of the elevator core structure. The elevator cars grip the structure without use of a track and are able to pass other cars enabling bi-directional traffic flow using a twisting motion. The freestanding tower can be used for launch activities, tourism, observation, wind-energy generation, scientific research, and communications.