Is anger a normal part of grief?
Yes. Anger is a common response to bereavement, frequently aimed at doctors, relatives, the world, the person who died, or yourself. It is not a mandatory stage of grief and not everyone experiences it, so its absence says nothing about your love or your grieving.
Anger is the least socially permitted grief emotion. Sadness gets sympathy; rage gets nervous silence. So people carry it privately and conclude something is wrong with them.
Where it comes from
Anger is often what helplessness becomes when helplessness is intolerable. Something enormous happened, you could not stop it, and fury at least has direction and energy. It is also, frequently, grief wearing armor: anger keeps you upright when sorrow would flatten you.
Who it lands on
Rarely the right target, because there usually is not one. It lands on the hospital, the sibling who visited less, the friend who said the wrong thing, the driver in front of you. It lands on the person who died, for smoking, for not going to the doctor, for leaving. And it lands on you, in the form of the sentences that start "if only I had." Anger at the dead is common and does not cancel out love; the two coexist in almost everyone who admits to it.
Anger is not stage two
The five-stages model put anger in a sequence, and that has done real damage: people wait for it, or feel defective when it does not arrive, or believe they must work through it to reach acceptance. The evidence does not support this. In Maciejewski and colleagues' 2007 study in JAMA, tracking bereaved people over two years, yearning was the dominant negative response throughout, not anger, and acceptance rose steadily from early on rather than arriving at the end. If you have never once been angry, nothing is missing (more on this in are the five stages real).
What to do with it
Anger wants discharge and expression, in that order. Discharge is physical: walking fast, lifting, swimming, anything that gives the body somewhere to put it. Expression is naming it accurately, ideally to a person or on paper: not "I am a bad person" but "I am furious that he did not go to the doctor when I asked, and I am terrified that being furious means I loved him badly." Anger that gets named tends to loosen. Anger with nowhere to go tends to arrive sideways, usually at the people still alive and standing near you.
When anger needs more than an article
Please speak to someone if anger is frightening you or others, if it is showing up as drinking more than you want to, or if it has fused with self-blame into something relentless. Rage that turns inward and stays there is worth professional attention, and grief-informed therapy is good at exactly this.
See also: Maciejewski et al. (2007) JAMA, testing the stage model; Kübler-Ross (1969) On Death and Dying, the origin of the stages; Stroebe & Schut (1999) Death Studies.