Based on the quasi physical model, two heuristic strategies are proposed for dealing with the equal sphere packing problem. The fake sphere strategy guarantees that the results are rigorous. The serial symmetrical relocation strategy is designed to search a dense feasible configuration from a local optimal configuration. Through a personal computer with Pentium E6500 2.93GHz CPU, the study has densely packed up to 200 equal spheres in spherical container and up to 150 equal spheres in cubic container. The obtained results not only have better quality than that of the international best known records, but also greatly outnumbered them. Particularly, the study packed 68 equal spheres of radius 1 into a large sphere whose radius is smaller than 5, thus proved wrong a conjecture which alleges a large sphere of radius 5 can contain at most 67 equal spheres of radius 1.