It is well known that a spherically symmetric imploding cold body collapses into a space-time singularity in general relativity. The singularity does not arise, however, in the modification of the theory proposed in C-field cosmology. Although the C-field has been used to represent creation of matter, the prevention of singularities does not depend on the creation property of the field, but on its negative energy density. It does not seem that singularities can be prevented except by a negative energy field. Internal pressures of the ordinary kind fail to provide support against gravitation provided the mass of the body is sufficiently large.