Generally selling the property and purchase another property are two separate and independent transactions...
And as a result - any gain you might have on the sale of the property is taxable gain.
What you likely means - section 1031 exchange - that allow to defer (not avoid!) taxes on the sale of the business or investment (not personal!) property.
A tax-deferred exchange is a method by which a property owner trades one or more relinquished properties for one or more replacement properties of "like-kind", while deferring the payment of federal income taxes and some state taxes on the transaction.
The like-kind exchange under Section 1031 is tax-deferred, not tax-free.
When the replacement property is ultimately sold (not as part of another exchange), the original deferred gain, plus any additional gain realized since the purchase of the replacement property, is subject to tax.
section 1031 lists following properties as not qualified - http://www4.law.cornell.edu/uscode/html/uscode26/usc_sec_26_00001031----000-.html
(A) stock in trade or other property held primarily for sale, (B) stocks, bonds, or notes, (C) other securities or evidences of indebtedness or interest, (D) interests in a partnership, (E) certificates of trust or beneficial interests, or (F) choses in action.
Section 1031 of the IRC provides that no gain or loss shall be recognized on the exchange of property held for productive use in a trade or business, or for investment.
Generally, for 1031 deferred like-kind exchange should be used an exchange accommodator as a third party to hold the proceeds from the sale and to purchase the new property. Sec. 1031 requires that within 45 days of the sale of the old property, that you must identify the replacement property and must complete the purchase of the replacement property within 180 days of the sale of the old property.
You may find more details here - http://www.1031.org/about1031/faq.htm