There are multiple theories to which one could apply a critical analysis of a poem. The theories that can be applied to poetry are the same which are applied to literature in general. The following literary theories are normally used when examining and criticising literature.
Moral Criticism (periods dating 360 BC to Present)-Based upon the thoughts of Plato and Aristotle. This theory looked at art (literature) in regards to its representation of moral good. Plato and Aristotle disagreed. For example, they disagreed that poets represent nature in a mediocre fashion.
New Criticism (periods dating 1930-Present)- These texts were examined in regards to their social or historical forces or ethical statements.
Psychoanalytic (1930-Present)-Based upon Freudian thought regarding the unconscious, the desires, and the defenses.
Marxist (1930- Present)-This theory focused upon social standing, personal values, and believability of the work.
Reader-Response (1960-Present)-This theory focuses upon the readers response to the text. Questions asked about the reading should focus upon reader interaction, reader experience, reader interpretation, and if the reader was acknowledged by the author.
Structuralism (1920-Present)- This theory examines the use of the linguistics and semiotics within a text. It also examines patterns and experiences within a text.
Deconstruction (1966-Present)-This theory examines how systems, frameworks and definitions are broken down for a reader.
New Historicism (1980-Present)-When using this theory, critics determine the importance of the time period, culture, and political movements which influenced the work.
Post-Colonial (1990-Present)-This theory focuses upon the literary works of people who were/are colonized and those in colonial power.
Feminist (1960-Present)-This theory examines the treatment of women in regards to political, economic, psychological, and social degradation and oppression.
Gender/Queer Studies (1970-Present)- This theory was influenced by Feminist theory and examines the "hows" in regard to the breakdowns of sexuality and gender bias.