  We construct a class of spherically symmetric collapse models in which a
naked singularity may develop as the end state of collapse. The matter
distribution considered has negative radial and tangential pressures, but the
weak energy condition is obeyed throughout. The singularity forms at the center
of the collapsing cloud and continues to be visible for a finite time. The
duration of visibility depends on the nature of energy distribution. Hence the
causal structure of the resulting singularity depends on the nature of the mass
function chosen for the cloud. We present a general model in which the naked
singularity formed is timelike, neither pointlike nor null. Our work represents
a step toward clarifying the necessary conditions for the validity of the
Cosmic Censorship Conjecture.
