The beaver occurs occasionally in heraldry, usually as a punning (or canting) device, e.g. in the family of "Beveridge". In contemporary "civic heraldry", it is not infrequent, said to represent industry. This was not the general opinion of 17th-century heralds. Guillim places the beaver among "exorbitant animals", and has this further to say of a crest bearing the beaver (keep in mind that the physical description at the end is as much of the heraldic beaver as of the natural):
He beareth Argent, a Bever erected Sable, devouring a Fish proper, Armed Gules. This Coat standeth in a glasse window in an Inne of Chancerie called New-in-Hall without Temple-Barre neere London. The Bever is like an Otter [a device borne by the family of Lutterell] and both of them are like slie dissembling companions, who to make their profit, and feed their owne bellies, will closely keepe a good quarter with contrarie sides, in affection to neither, but onely for their owne behoofe: therefore I could wish they had one other property of the bever, which is to geld himselfe, that so he might escape from his pursuers, who hunt him for his testicles, which are much used in Physicke. This Bever hath only his taile fish, and therfore keepes that part most in the water: he hath his hinder legges like a Swanne, and his former like a Dogge, and so swimmeth with the one whiles hee preieth with the other.
John Guillim, Description of Heraldrie (1610), p. 178 (Sect. III, Chap. 25).
Blome's Art of Heraldry, which says it is organized "according to the excellent Method of Guillim's HERALDRY" and is in fact an abridgement of Guillim, removes the specific instance of the shield and the disobliging remarks, including its alleged propensity for self-castration, under "Monstrous Creatures":
1. Argent, a Beaver erected Sable, devouring a Fish, proper.
The Beaver hath his Tail only Fish, which he keeps for the most part in the Water, his hinder Leggs are like a Swan, and his foremost like a Dogg; so he swims with the one, whilst he preyeth with the other.
Richard Blome, Art of Heraldry (1685), p. 195.
In the representations below, notice that the beaver is entire — indeed, unanatomically so (for a beaver) (click on the third shield for a larger view).
Beaver 1: "John Logan", A display of heraldry manifesting a more easie access to the knowledge thereof than hath been hitherto published by any, through the benefit of method, etc. 1679, p. 189.
Beaver 2: Guillim, Display of Heraldry 1611, p. 178.
Beaver 3: Guillim, Display of Heraldry 1664, p. 253.
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